A Momentous Arrow of Time (2009)
Quantum cosmology offers a unique stage to address questions of time related to its underlying (and perhaps truly quantum dynamical) meaning as well as its origin. Some of these issues can be...
Quantum geometry and quantum dynamics at the Planck scale (2009)
Canonical quantum gravity provides insights into the quantum dynamics as well as quantum geometry of space-time by its implications for constraints. Loop quantum gravity in particular requires...
Group Theoretical Quantization and the Example of a Phase Space (2009)
Martin Bojowald, Thomas Strobl, Thomas Strobly
Phase Space S 1 \Theta R+
CGPG–01/12–1 Poisson Geometry in Constrained Systems (2009)
The Erwin, Schrödinger International Boltzmanngasse, Martin Bojowald, Thomas Strobl, Martin Bojowald A, Thomas Strobl B
Associated to a constrained system with closed constraint algebra there are two Poisson manifolds P and Q forming a symplectic dual pair with respect to the original, unconstrained phase space: P is...
Spherically Symmetric Quantum Geometry: States and Basic (2009)
Abstract The kinematical setting of spherically symmetric quantum geometry, derived from the full theory of loop quantum gravity, is developed. This extends previous studies of homogeneous models to...
Spin foam quantization and anomalies (2009)
Martin Bojowald, Alejandro Perez, Martin Bojowald
\Lambda and Alejandro Perez y
Symplectic Cuts and Projection Quantization (2009)
Martin Bojowald, Thomas Strobl
Abstract The recently proposed projection quantization, which is a method to quantize particular subspaces of systems with known quantum theory, is shown to yield a genuine quantization in several...
The Volume Operator in Spherically Symmetric Quantum Geometry (2009)
Martin Bojowald, Rafal Swiderski, Martin Bojowald
and Rafal Swiderski y Max-Planck-Institut f"ur Gravitationsphysik, Albert-Einstein-Institut,
Non-marginal LTB-like models with inverse triad corrections from loop quantum gravity (2009)
Bojowald, Martin, Reyes, Juan D., Tibrewala, Rakesh
Marginal LTB models with corrections from loop quantum gravity have recently been studied with an emphasis on potential singularity resolution. This paper corroborates and extends the analysis in two...
Effective Constraints for Relativistic Quantum Systems (2009)
Bojowald, Martin, Tsobanjan, Artur
Determining the physical Hilbert space is often considered the most difficult but crucial part of completing the quantization of a constrained system. In such a situation it can be more economical to...
Consistent Loop Quantum Cosmology (2008)
A consistent combination of quantum geometry effects rules out a large class of models of loop quantum cosmology and their critical densities as they have been used in the recent literature. In...
Comment on "Quantum bounce and cosmic recall" [arXiv:0710.4543] (2008)
A recently derived inequality on volume fluctuations of a bouncing cosmology, valid for states which are semiclassical long after the bounce, does not restrict pre-bounce fluctuations sufficiently...
Bojowald, Martin, Hossain, Golam Mortuza, Kagan, Mikhail, Shankaranarayanan, S.
A consistent implementation of quantum gravity is expected to change the familiar notions of space, time and the propagation of matter in drastic ways. This will have consequences on very small...
Dilaton Gravity, Poisson Sigma Models and Loop Quantum Gravity (2008)
Bojowald, Martin, Reyes, Juan D.
Spherically symmetric gravity in Ashtekar variables coupled to Yang-Mills theory in two dimensions and its relation to dilaton gravity and Poisson sigma models are discussed. After introducing its...
Effective theory for the cosmological generation of structure (2008)
Bojowald, Martin, Skirzewski, Aureliano
The current understanding of structure formation in the early universe is mainly built on a magnification of quantum fluctuations in an initial vacuum state during an early phase of accelerated...
Canonical Relativity and the Dimensionality of the World (2008)
Different aspects of relativity, mainly in a canonical formulation, relevant for the question "Is spacetime nothing more than a mathematical space (which describes the evolution in time of the...
Quantum gravity is expected to be necessary in order to understand situations in which classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities,...
Anomaly freedom in perturbative loop quantum gravity (2008)
Bojowald, Martin, Hossain, Golam Mortuza, Kagan, Mikhail, Shankaranarayanan, S.
A fully consistent linear perturbation theory for cosmology is derived in the presence of quantum corrections as they are suggested by properties of inverse volume operators in loop quantum gravity....
Fermions in Loop Quantum Cosmology and the Role of Parity (2008)
Fermions play a special role in homogeneous models of quantum cosmology because the exclusion principle prevents them from forming sizable matter contributions. They can thus describe the matter...
Lemaitre-Tolman-Bondi collapse from the perspective of loop quantum gravity (2008)
Bojowald, Martin, Harada, Tomohiro, Tibrewala, Rakesh
Lemaitre-Tolman-Bondi models as specific spherically symmetric solutions of general relativity simplify in their reduced form some of the mathematical ingredients of black hole or cosmological...
How quantum is the big bang? (2008)
When quantum gravity is used to discuss the big bang singularity, the most important, though rarely addressed, question is what role genuine quantum degrees of freedom play. Here, complete effective...
Effective Constraints for Quantum Systems (2008)
Bojowald, Martin, Sandhoefer, Barbara, Skirzewski, Aureliano, Tsobanjan, Artur
An effective formalism for quantum constrained systems is presented which allows manageable derivations of solutions and observables, including a treatment of physical reality conditions without...
Recollapsing quantum cosmologies and the question of entropy (2008)
Bojowald, Martin, Tavakol, Reza
Recollapsing homogeneous and isotropic models present one of the key ingredients for cyclic scenarios. This is considered here within a quantum cosmological framework in presence of a free scalar...
Loop Quantum Cosmology: Effective theories and oscillating universes (2008)
Bojowald, Martin, Tavakol, Reza
Despite its great successes in accounting for the current observations, the so called `standard' model of cosmology faces a number of fundamental unresolved questions. Paramount among these are those...
Quantum nature of cosmological bounces (2008)
Several examples are known where quantum gravity effects resolve the classical big bang singularity by a bounce. The most detailed analysis has probably occurred for loop quantum cosmology of...
Summary of session D2: quantum aspects of cosmology (2008)
This is a summary of talks about quantum aspects of cosmology. Topics involve the properties of quantum matter fields on an expanding spacetime as well as issues in the quantization of gravity...
Quantum gravity is expected to be necessary in order to understand situations in which classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities,...
Symplectic Cuts and Projection Quantization (2007)
The Erwin, Schrodinger International Boltzmanngasse, Thomas Strobl, Martin Bojowald, Martin Bojowald
and Thomas Strobl by a
The radiation equation of state and loop quantum gravity corrections (2007)
The equation of state for radiation is derived in a canonical formulation of the electromagnetic field. This allows one to include correction terms expected from canonical quantum gravity and to...
Canonical Gravity with Fermions (2007)
Canonical gravity in real Ashtekar-Barbero variables is generalized to allow for fermionic matter. The resulting torsion changes several expressions in Holst's original vacuum analysis, which are...
Dirac Fields in Loop Quantum Gravity and Big Bang Nucleosynthesis (2007)
Bojowald, Martin, Das, Rupam, Scherrer, Robert J.
Big Bang nucleosynthesis requires a fine balance between equations of state for photons and relativistic fermions. Several corrections to equation of state parameters arise from classical and quantum...
Harmonic cosmology: How much can we know about a universe before the big bang? (2007)
Quantum gravity may remove classical space-time singularities and thus reveal what a universe at and before the big bang could be like. In loop quantum cosmology, an exactly solvable model is...
Loop quantum gravity corrections to gravitational wave dispersion (2007)
Bojowald, Martin, Hossain, Golam Mortuza
Cosmological tensor perturbations equations are derived for Hamiltonian cosmology based on Ashtekar's formulation of general relativity, including typical quantum gravity effects in the Hamiltonian...
Cosmological vector modes and quantum gravity effects (2007)
Bojowald, Martin, Hossain, Golam Mortuza
In contrast to scalar and tensor modes, vector modes of linear perturbations around an expanding Friedmann--Robertson--Walker universe decay. This makes them largely irrelevant for late time...
Effective equations for isotropic quantum cosmology including matter (2007)
Bojowald, Martin, Hernandez, Hector, Skirzewski, Aureliano
Effective equations often provide powerful tools to develop a systematic understanding of detailed properties of a quantum system. This is especially helpful in quantum cosmology where several...
The Dark Side of a Patchwork Universe (2007)
While observational cosmology has recently progressed fast, it revealed a serious dilemma called dark energy: an unknown source of exotic energy with negative pressure driving a current accelerating...
Lattice refining loop quantum cosmology, anisotropic models and stability (2007)
Bojowald, Martin, Cartin, Daniel, Khanna, Gaurav
A general class of loop quantizations for anisotropic models is introduced and discussed, which enhances loop quantum cosmology by relevant features seen in inhomogeneous situations. The main new...
Dynamical coherent states and physical solutions of quantum cosmological bounces (2007)
A new model is studied which describes the quantum behavior of transitions through an isotropic quantum cosmological bounce in loop quantum cosmology sourced by a free and massless scalar field. As...
Singularities and Quantum Gravity (2007)
Although there is general agreement that a removal of classical gravitational singularities is not only a crucial conceptual test of any approach to quantum gravity but also a prerequisite for any...
Quantum gravity and cosmological observations (2007)
Quantum gravity places entirely new challenges on the formulation of a consistent theory as well as on an extraction of potentially observable effects. Quantum corrections due to the gravitational...
Formation and Evolution of Structure in Loop Cosmology (2007)
Bojowald, Martin, Hernandez, Hector H., Kagan, Mikhail, Singh, Parampreet, Skirzewski, Aureliano
Inhomogeneous cosmological perturbation equations are derived in loop quantum gravity, taking into account corrections in particular in gravitational parts. This provides a framework for calculating...
Effective constraints of loop quantum gravity (2007)
Bojowald, Martin, Hernandez, Hector H., Kagan, Mikhail, Singh, Parampreet, Skirzewski, Aureliano
Within a perturbative cosmological regime of loop quantum gravity corrections to effective constraints are computed. This takes into account all inhomogeneous degrees of freedom relevant for scalar...
Quantum gravity and higher curvature actions (2007)
Bojowald, Martin, Skirzewski, Aureliano
Effective equations are often useful to extract physical information from quantum theories without having to face all technical and conceptual difficulties. One can then describe aspects of the...
Formation and Evolution of Structure in Loop Cosmology (2006)
Bojowald, Martin, Hernandez, Hector, Kagan, Mikhail, Singh, Parampreet, Skirzewski, Aureliano
Inhomogeneous cosmological perturbation equations are derived in loop quantum gravity, taking into account corrections in particular in gravitational parts. This provides a framework for calculating...
Effective constraints of loop quantum gravity (2006)
Bojowald, Martin, Hernandez, Hector, Kagan, Mikhail, Skirzewski, Aureliano
Within a perturbative cosmological regime of loop quantum gravity corrections to effective constraints are computed. This takes into account all inhomogeneous degrees of freedom relevant for scalar...
Hamiltonian cosmological perturbation theory with loop quantum gravity corrections (2006)
Bojowald, Martin, Hernández, Hector H., Kagan, Mikhail, Singh, Parampreet, Skirzewski, Aureliano
Cosmological perturbation equations are derived systematically in a canonical scheme based on Ashtekar variables. A comparison with the covariant derivation and various subtleties in the calculation...
Loop quantum cosmology and inhomogeneities (2006)
Inhomogeneities are introduced in loop quantum cosmology using regular lattice states, with a kinematical arena similar to that in homogeneous models considered earlier. The framework is intended to...
Large scale effective theory for cosmological bounces (2006)
An exactly solvable bounce model in loop quantum cosmology is identified which serves as a perturbative basis for realistic bounce scenarios. Its bouncing solutions are derived analytically,...
Quantum Geometry and its Implications for Black Holes (2006)
General relativity successfully describes space-times at scales that we can observe and probe today, but it cannot be complete as a consequence of singularity theorems. For a long time there have...
Quantum Gravity and Higher Curvature Actions (2006)
Bojowald, Martin, Skirzewski, Aureliano
Effective equations are often useful to extract physical information from quantum theories without having to face all technical and conceptual difficulties. One can then describe aspects of the...
Loop cosmological implications of a non-minimally coupled scalar field (2006)
Bojowald, Martin, Kagan, Mikhail
Non-minimal actions with matter represented by a scalar field coupled to gravity are considered in the context of a homogeneous and isotropic universe. The coupling is of the form $-\xi/2 \phi^2 R$....
Quantum cosmology in general denotes the application of quantum physics to the whole universe and thus gives rise to many realizations and examples, covering problems at different mathematical and...
Quantum Riemannian Geometry and Black Holes (2006)
Black Holes have always played a central role in investigations of quantum gravity. This includes both conceptual issues such as the role of classical singularities and information loss, and...
Quantum gravity is expected to be necessary in order to understand situations where classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities,...
Non-Singular Quantum Geometry of the Schwarzschild Black Hole Interior (2006)
Ashtekar,Abhay, Bojowald,Martin
In homogeneous cosmologies, quantum geometry effects lead to a resolution of the classical singularity without having to invoke special boundary conditions at the singularity or introduce ad-hoc...
Spherically Symmetric Quantum Geometry: Hamiltonian Constraint (2006)
Bojowald,Martin, Swiderski,Rafal
Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all...
Non-Singular Quantum Geometry of the Schwarzschild Black Hole Interior (2006)
Ashtekar, Abhay, Bojowald, Martin
In homogeneous cosmologies, quantum geometry effects lead to a resolution of the classical singularity without having to invoke special boundary conditions at the singularity or introduce ad-hoc...
Degenerate Configurations, Singularities and the Non-Abelian Nature of Loop Quantum Gravity (2006)
Degenerate geometrical configurations in quantum gravity are important to understand if the fate of classical singularities is to be revealed. However, not all degenerate configurations arise on an...
Universe scenarios from loop quantum cosmology (2006)
Loop quantum cosmology is an application of recent developments for a non-perturbative and background independent quantization of gravity to a cosmological setting. Characteristic properties of the...
Effective Equations of Motion for Quantum Systems (2006)
Bojowald, Martin, Skirzewski, Aureliano
In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary...
Perturbative Degrees of Freedom in Loop Quantum Gravity: Anisotropies (2006)
Bojowald, Martin, Hernandez, Hector H., Morales-Tecotl, Hugo A.
The relation between an isotropic and an anisotropic model in loop quantum cosmology is discussed in detail, comparing the strict symmetry reduction with a perturbative implementation of symmetry....
Spherically Symmetric Quantum Geometry: Hamiltonian Constraint (2006)
Bojowald, Martin, Swiderski, Rafal
Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all...
Quantum Riemannian Geometry and Black Holes (2006)
Black Holes have always played a central role in investigations of quantum gravity. This includes both conceptual issues such as the role of classical singularities and information loss, and...
Hamiltonian cosmological perturbation theory with loop quantum gravity corrections (2006)
Bojowald, Martin, Hernandez, Hector H., Kagan, Mikhail, Singh, Parampreet, Skirzewski, Aureliano
Cosmological perturbation equations are derived systematically in a canonical scheme based on Ashtekar variables. A comparison with the covariant derivation and various subtleties in the calculation...
Quantum geometry and the Schwarzschild singularity (2006)
Ashtekar, Abhay, Bojowald, Martin
In homogeneous cosmologies, quantum geometry effects lead to a resolution of the classical singularity without having to invoke special boundary conditions at the singularity or introduce ad hoc...
Quantum geometry and its implications for black holes (2006)
General relativity successfully describes space–times at scales that we can observe and probe today, but it cannot be complete as a consequence of singularity theorems. For a long time, there have...
Quantum gravity is expected to be necessary in order to understand situations where classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities,...
Universe scenarios from loop quantum cosmology (2005)
Loop quantum cosmology is an application of recent developments for a non-perturbative and background independent quantization of gravity to a cosmological setting. Characteristic properties of the...
Spherically Symmetric Quantum Geometry: Hamiltonian Constraint (2005)
Bojowald, Martin, Swiderski, Rafal
Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all...
Perturbative Degrees of Freedom in Loop Quantum Gravity: Anisotropies (2005)
Bojowald, Martin, Hernandez, Hector H., Morales-Tecotl, Hugo A
The relation between an isotropic and an anisotropic model in loop quantum cosmology is discussed in detail, comparing the strict symmetry reduction with a perturbative implementation of symmetry....
Effective Equations of Motion for Quantum Systems (2005)
Bojowald, Martin, Skirzewski, Aureliano
In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary...
Quantum geometry and the Schwarzschild singularity (2005)
Ashtekar, Abhay, Bojowald, Martin
In homogeneous cosmologies, quantum geometry effects lead to a resolution of the classical singularity without having to invoke special boundary conditions at the singularity or introduce ad-hoc...
Degenerate Configurations, Singularities and the Non-Abelian Nature of Loop Quantum Gravity (2005)
Degenerate geometrical configurations in quantum gravity are important to understand if the fate of classical singularities is to be revealed. However, not all degenerate configurations arise on an...
Black hole evaporation: A paradigm (2005)
Ashtekar,Abhay, Bojowald,Martin
A paradigm describing black hole evaporation in non-perturbative quantum gravity is developed by combining two sets of detailed results: i) resolution of the Schwarzschild singularity in loop quantum...
Lie algebroid morphisms, Poisson Sigma Models, and off-shell closed gauge symmetries (2005)
Bojowald,Martin, Kotov,Alexei, Strobl,Thomas
Chern-Simons gauge theories in 3 dimensions and the Poisson Sigma Model (PSM) in 2 dimensions are examples of the same theory, if their field equations are interpreted as morphisms of Lie algebroids...
Nonsingular Black Holes and Degrees of Freedom in Quantum Gravity (2005)
Spherically symmetric space-times provide many examples for interesting black hole solutions, which classically are all singular. Following a general program, space-like singularities in spherically...
Elements of Loop Quantum Cosmology (2005)
The expansion of our universe, when followed backward in time, implies that it emerged from a phase of huge density, the big bang. These stages are so extreme that classical general relativity...
Asymptotic Properties of Difference Equations for Isotropic Loop Quantum Cosmology (2005)
In loop quantum cosmology, a difference equation for the wave function describes the evolution of a universe model. This is different from the differential equations that arise in Wheeler-DeWitt...
Black hole evaporation: A paradigm (2005)
Ashtekar, Abhay, Bojowald, Martin
A paradigm describing black hole evaporation in non-perturbative quantum gravity is developed by combining two sets of detailed results: i) resolution of the Schwarzschild singularity using quantum...
A black hole mass threshold from non-singular quantum gravitational collapse (2005)
Bojowald, Martin, Goswami, Rituparno, Maartens, Roy, Singh, Parampreet
Quantum gravity is expected to remove the classical singularity that arises as the end-state of gravitational collapse. To investigate this, we work with a toy model of a collapsing homogeneous...
The Early Universe in Loop Quantum Cosmology (2005)
Loop quantum cosmology applies techniques derived for a background independent quantization of general relativity to cosmological situations and draws conclusions for the very early universe. Direct...
Spherically Symmetric Quantum Horizons (2005)
Bojowald,Martin, Swiderski,Rafal
Isolated horizon conditions specialized to spherical symmetry can be imposed directly at the quantum level. This answers several questions concerning horizon degrees of freedom, which are seen to be...
On Loop Quantum Gravity Phenomenology and the Issue of Lorentz Invariance (2005)
Bojowald,Martin, Morales-Tecotl,Hugo A., Sahlmann,Hanno
A simple model is constructed which allows to compute modified dispersion relations with effects from loop quantum gravity. Different quantization choices can be realized and their effects on the...
A black hole mass threshold from non-singular quantum gravitational collapse (2005)
Bojowald,Martin, Goswami,Rituparno, Maartens,Roy, Singh,Parampreet
Quantum gravity is expected to remove the classical singularity that arises as the end-state of gravitational collapse. To investigate this, we work with a simple toy model of a collapsing...
Asymptotic Properties of Difference Equations for Isotropic Loop Quantum Cosmology (2005)
In loop quantum cosmology, a difference equation for the wave function describes the evolution of a universe model. This is different from the differential equations that arise in Wheeler-DeWitt...
Lie algebroid morphisms, Poisson Sigma Models, and off-shell closed gauge symmetries (2005)
Bojowald, Martin, Kotov, Alexei, Strobl, Thomas
Chern-Simons gauge theories in 3 dimensions and the Poisson Sigma Model (PSM) in 2 dimensions are examples of the same theory, if their field equations are interpreted as morphisms of Lie algebroids...
Black hole evaporation: A paradigm (2005)
Ashtekar, Abhay, Bojowald, Martin
A paradigm describing black hole evaporation in non-perturbative quantum gravity is developed by combining two sets of detailed results: i) resolution of the Schwarzschild singularity in loop quantum...
Spherically Symmetric Quantum Horizons (2005)
Bojowald, Martin, Swiderski, Rafal
Isolated horizon conditions specialized to spherical symmetry can be imposed directly at the quantum level. This answers several questions concerning horizon degrees of freedom, which are seen to be...
On Loop Quantum Gravity Phenomenology and the Issue of Lorentz Invariance (2005)
Bojowald, Martin, Morales-Tecotl, Hugo A., Sahlmann, Hanno
A simple model is constructed which allows to compute modified dispersion relations with effects from loop quantum gravity. Different quantization choices can be realized and their effects on the...
A black hole mass threshold from non-singular quantum gravitational collapse (2005)
Bojowald, Martin, Goswami, Rituparno, Maartens, Roy, Singh, Parampreet
Quantum gravity is expected to remove the classical singularity that arises as the end-state of gravitational collapse. To investigate this, we work with a simple toy model of a collapsing...
The Early Universe in Loop Quantum Cosmology (2005)
Loop quantum cosmology applies techniques derived for a background independent quantization of general relativity to cosmological situations and draws conclusions for the very early universe. Direct...
The expansion of our universe, when followed backward in time, implies that it emerged from a phase of huge density, the big bang. These stages are so extreme that classical general relativity...
Asymptotic Properties of Difference Equations for Isotropic Loop Quantum Cosmology (2005)
In loop quantum cosmology, a difference equation for the wave function describes the evolution of a universe model. This is different from the differential equations that arise in Wheeler-DeWitt...
Nonsingular Black Holes and Degrees of Freedom in Quantum Gravity (2005)
Spherically symmetric space-times provide many examples for interesting black hole solutions, which classically are all singular. Following a general program, space-like singularities in spherically...
The lack of a coherent quantum description of gravity has impeded our understanding of the physics that determined how the Universe began. A synthesis of recent ideas may take us a step farther back...
Quantum gravity is expected to be necessary in order to understand situations where classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities,...
On Loop Quantum Gravity Phenomenology and the Issue of Lorentz Invariance (2004)
Bojowald, Martin, Morales-Tecotl, Hugo A., Sahlmann, Hanno
A simple model is constructed which allows to compute modified dispersion relations with effects from loop quantum gravity. Different quantization choices can be realized and their effects on the...
Spherically Symmetric Quantum Horizons (2004)
Bojowald, Martin, Swiderski, Rafal
Isolated horizon conditions specialized to spherical symmetry can be imposed directly at the quantum level. This answers several questions concerning horizon degrees of freedom, which are seen to be...
Coordinate time dependence in Quantum Gravity (2004)
Bojowald, Martin, Singh, Parampreet, Skirzewski, Aureliano
The intuitive classical space-time picture breaks down in quantum gravity, which makes a comparison and the development of semiclassical techniques quite complicated. Using ingredients of the group...
Loop Quantum Gravity and the Cyclic Universe (2004)
Bojowald, Martin, Maartens, Roy, Singh, Parampreet
Loop quantum gravity introduces strong non-perturbative modifications to the dynamical equations in the semi-classical regime, which are responsible for various novel effects, including resolution of...
Spherically Symmetric Quantum Geometry: States and Basic Operators (2004)
The kinematical setting of spherically symmetric quantum geometry, derived from the full theory of loop quantum gravity, is developed. This extends previous studies of homogeneous models to...
The Volume Operator in Spherically Symmetric Quantum Geometry (2004)
Bojowald, Martin, Swiderski, Rafal
The spherically symmetric volume operator is discussed and all its eigenstates and eigenvalues are computed. Even though the operator is more complicated than its homogeneous analog, the spectra are...
Lie algebroid morphisms, Poisson Sigma Models, and off-shell closed gauge symmetries (2004)
Bojowald, Martin, Kotov, Alexei, Strobl, Thomas
Chern-Simons gauge theories in 3 dimensions and the Poisson Sigma Model (PSM) in 2 dimensions are examples of the same theory, if their field equations are interpreted as morphisms of Lie algebroids...
Generating function techniques for loop quantum cosmology (2004)
Cartin, Daniel, Khanna, Gaurav, Bojowald, Martin
Loop quantum cosmology leads to a difference equation for the wave function of a universe, which in general has solutions changing rapidly even when the volume changes only slightly. For a...
The Bianchi IX model in Loop Quantum Cosmology (2004)
Bojowald, Martin, Date, Ghanashyam, Hossain, Golam Mortuza
The Bianchi IX model has been used often to investigate the structure close to singularities of general relativity. Its classical chaos is expected to have, via the BKL scenario, implications even...
Inflationary Cosmology and Quantization Ambiguities in Semi-Classical Loop Quantum Gravity (2004)
Bojowald, Martin, Lidsey, James E., Mulryne, David J., Singh, Parampreet, Tavakol, Reza
In loop quantum gravity, modifications to the geometrical density cause a self-interacting scalar field to accelerate away from a minimum of its potential. In principle, this mechanism can generate...
Loop Quantum Cosmology: Recent Progress (2004)
Aspects of the full theory of loop quantum gravity can be studied in a simpler context by reducing to symmetric models like cosmological ones. This leads to several applications where loop effects...
Inflationary Cosmology and Quantization Ambiguities in Semi-Classical Loop Quantum Gravity (2004)
Bojowald,Martin, Lidsey,James E., Mulryne,David J., Singh,Parampreet, Tavakol,Reza
In loop quantum gravity, modifications to the geometrical density cause a self-interacting scalar field to accelerate away from a minimum of its potential. In principle, this mechanism can generate...
The Bianchi IX model in Loop Quantum Cosmology (2004)
Bojowald,Martin, Date,Ghanashyam, Hossain,Golam Mortuza
The Bianchi IX model has been used often to investigate the structure close to singularities of general relativity. Its classical chaos is expected to have, via the BKL scenario, implications even...
Generating function techniques for loop quantum cosmology (2004)
Cartin,Daniel, Khanna,Gaurav, Bojowald,Martin
Loop quantum cosmology leads to a difference equation for the wave function of a universe. In the semiclassical limit, small-scale oscillations must be suppressed by choosing parameters of general...
The Volume Operator in Spherically Symmetric Quantum Geometry (2004)
Bojowald,Martin, Swiderski,Rafal
The spherically symmetric volume operator is discussed and all its eigenstates and eigenvalues are computed. Even though the operator is more complicated than its homogeneous analog, the spectra are...
Loop Quantum Gravity and the Cyclic Universe (2004)
Bojowald,Martin, Maartens,Roy, Singh,Parampreet
Loop quantum gravity introduces strong non-perturbative modifications to the dynamical equations in the semi-classical regime, which are responsible for various novel effects, including resolution of...
Time dependence in Quantum Gravity (2004)
Bojowald,Martin, Singh,Parampreet, Skirzewski,Aureliano
The intuitive classical space-time picture breaks down in quantum gravity, which makes a comparison and the development of semiclassical techniques quite complicated. By a variation of the group...
Quantum Gravity and the Big Bang (2004)
Quantum gravity has matured over the last decade to a theory which can tell in a precise and explicit way how cosmological singularities of general relativity are removed. A branch of the universe...
Loop Quantum Cosmology: Recent Progress (2004)
Aspects of the full theory of loop quantum gravity can be studied in a simpler context by reducing to symmetric models like cosmological ones. This leads to several applications where loop effects...
Inflationary Cosmology and Quantization Ambiguities in Semi-Classical Loop Quantum Gravity (2004)
Bojowald, Martin, Lidsey, James E., Mulryne, David J., Singh, Parampreet, Tavakol, Reza
In loop quantum gravity, modifications to the geometrical density cause a self-interacting scalar field to accelerate away from a minimum of its potential. In principle, this mechanism can generate...
The Bianchi IX model in Loop Quantum Cosmology (2004)
Bojowald, Martin, Date, Ghanashyam, Hossain, Golam Mortuza
The Bianchi IX model has been used often to investigate the structure close to singularities of general relativity. Its classical chaos is expected to have, via the BKL scenario, implications even...
Generating function techniques for loop quantum cosmology (2004)
Cartin, Daniel, Khanna, Gaurav, Bojowald, Martin
Loop quantum cosmology leads to a difference equation for the wave function of a universe. In the semiclassical limit, small-scale oscillations must be suppressed by choosing parameters of general...
Spherically Symmetric Quantum Geometry: States and Basic Operators (2004)
The kinematical setting of spherically symmetric quantum geometry, derived from the full theory of loop quantum gravity, is developed. This extends previous studies of homogeneous models to...
The Volume Operator in Spherically Symmetric Quantum Geometry (2004)
Bojowald, Martin, Swiderski, Rafal
The spherically symmetric volume operator is discussed and all its eigenstates and eigenvalues are computed. Even though the operator is more complicated than its homogeneous analog, the spectra are...
Loop Quantum Gravity and the Cyclic Universe (2004)
Bojowald, Martin, Maartens, Roy, Singh, Parampreet
Loop quantum gravity introduces strong non-perturbative modifications to the dynamical equations in the semi-classical regime, which are responsible for various novel effects, including resolution of...
Time dependence in Quantum Gravity (2004)
Bojowald, Martin, Singh, Parampreet, Skirzewski, Aureliano
The intuitive classical space-time picture breaks down in quantum gravity, which makes a comparison and the development of semiclassical techniques quite complicated. By a variation of the group...
Coordinate time dependence in quantum gravity (2004)
Bojowald, Martin, Singh, Parampreet, Skirzewski, Aureliano
The intuitive classical space-time picture breaks down in quantum gravity, which makes a comparison and the development of semiclassical techniques quite complicated. Using ingredients of the group...
Spherically Symmetric Quantum Geometry: States and Basic Operators (2004)
The kinematical setting of spherically symmetric quantum geometry, derived from the full theory of loop quantum gravity, is developed. This extends previous studies of homogeneous models to...
The Volume Operator in Spherically Symmetric Quantum Geometry (2004)
Martin Bojowald, Rafal Swiderski
The spherically symmetric volume operator is discussed and all its eigenstates and eigenvalues are computed. Even though the operator is more complicated than its homogeneous analog, the spectra are...
Lie algebroid morphisms, Poisson Sigma Models, (2004)
The Erwin, Schrödinger International Boltzmanngasse, Martin Bojowald, Alexei Kotov, Thomas Strobl, Martin Bojowald A, ...
and o-shell closed gauge symmetries
Lie algebroid morphisms, Poisson Sigma Models, and off-shell closed gauge symmetries (2004)
Martin Bojowald, Alexei Kotov, Thomas Strobl, Martin Bojowalda, Alexei Kotovb, Thomas Stroblb
Lie algebroid morphisms, Poisson Sigma Models,and o ff-shell closed gauge symmetries
Loop Quantum Cosmology and Boundary Proposals (2003)
Bojowald, Martin, Vandersloot, Kevin
For many years, the most active area of quantum cosmology has been the issue of choosing boundary conditions for the wave function of a universe. Recently, loop quantum cosmology, which is obtained...
Quantum suppression of the generic chaotic behavior close to cosmological singularities (2003)
Bojowald, Martin, Date, Ghanashyam
In classical general relativity, the generic approach to the initial singularity is very complicated as exemplified by the chaos of the Bianchi IX model which displays the generic local evolution...
Homogeneous Loop Quantum Cosmology: The Role of the Spin Connection (2003)
Bojowald, Martin, Date, Ghanashyam, Vandersloot, Kevin
Homogeneous cosmological models with non-vanishing intrinsic curvature require a special treatment when they are quantized with loop quantum cosmological methods. Guidance from the full theory which...
Quantum Gravity and the Big Bang (2003)
Quantum gravity has matured over the last decade to a theory which can tell in a precise and explicit way how cosmological singularities of general relativity are removed. A branch of the universe...
Consistency Conditions for Fundamentally Discrete Theories (2003)
Bojowald, Martin, Date, Ghanashyam
The dynamics of physical theories is usually described by differential equations. Difference equations then appear mainly as an approximation which can be used for a numerical analysis. As such, they...
Cosmological applications of loop quantum gravity (2003)
Bojowald, Martin, Morales-Tecotl, Hugo A.
After a brief introduction to classical and quantum gravity we discuss applications of loop quantum gravity in the cosmological realm. This includes the basic formalism and recent results of loop...
Initial Conditions for a Universe (2003)
In physical theories, boundary or initial conditions play the role of selecting special situations which can be described by a theory with its general laws. Cosmology has long been suspected to be...
Classical Solutions for Poisson Sigma Models on a Riemann surface (2003)
Bojowald, Martin, Strobl, Thomas
We determine the moduli space of classical solutions to the field equations of Poisson Sigma Models on arbitrary Riemann surfaces for Poisson structures with vanishing Poisson form class. This...
Mathematical structure of loop quantum cosmology (2003)
Ashtekar, Abhay, Bojowald, Martin, Lewandowski, Jerzy
Applications of Riemannian quantum geometry to cosmology have had notable successes. In particular, the fundamental discreteness underlying quantum geometry has led to a natural resolution of the big...
Mathematical structure of loop quantum cosmology (2003)
Ashtekar, Abhay, Bojowald, Martin, Lewandowski, Jerzy
Applications of Riemannian quantum geometry to cosmology have had notable successes. In particular, the fundamental discreteness underlying quantum geometry has led to a natural resolution of the big...
Loop Quantum Cosmology, Boundary Proposals, and Inflation (2003)
Bojowald, Martin, Vandersloot, Kevin
Loop quantum cosmology of the closed isotropic model is studied with a special emphasis on a comparison with traditional results obtained in the Wheeler-DeWitt approach. This includes the relation of...
Homogeneous Loop Quantum Cosmology (2003)
Loop quantum cosmological methods are extended to homogeneous models in diagonalized form. It is shown that the diagonalization leads to a simplification of the volume operator such that its spectrum...
Spin Foam Quantization and Anomalies (2003)
Bojowald, Martin, Perez, Alejandro
The most common spin foam models of gravity are widely believed to be discrete path integral quantizations of the Plebanski action. However, their derivation in present formulations is incomplete and...
Classically, the approach to a singularity in general relativity is very complicated, as illustrated by the chaotic Bianchi IX model. Quantum gravity effects can potentially change the behavior and...
Homogeneous Loop Quantum Cosmology (2003)
Bojowald,Martin, Date,G., Vandersloot,K.
Homogeneous cosmological models with non-vanishing intrinsic curvature require a special treatment when they are quantized with loop quantum cosmological methods. Guidance from the full theory which...
Bojowald, Martin, Date, Ghanashyam
Classically, the approach to a singularity in general relativity is very complicated, as illustrated by the chaotic Bianchi IX model. Quantum gravity effects can potentially change the behavior and...
Homogeneous Loop Quantum Cosmology (2003)
Bojowald, Martin, Date, Ghanashyam, Vandersloot, K.
Homogeneous cosmological models with non-vanishing intrinsic curvature require a special treatment when they are quantized with loop quantum cosmological methods. Guidance from the full theory which...
Spin Foam Quantization and Anomalies (2003)
Martin Bojowald, Alejandro Perez
The most common spin foam models of gravity are widely believed to be discrete path integral quantizations of the Plebanski action. However, their derivation in present formulations is incomplete and...
Isotropic Loop Quantum Cosmology with Matter (2002)
Bojowald, Martin, Hinterleitner, Franz
A free massless scalar field is coupled to homogeneous and isotropic loop quantum cosmology. The coupled model is investigated in the vicinity of the classical singularity, where discreteness is...
Quantization Ambiguities in Isotropic Quantum Geometry (2002)
Some typical quantization ambiguities of quantum geometry are studied within isotropic models. Since this allows explicit computations of operators and their spectra, one can investigate the effects...
Inflation from Quantum Geometry (2002)
Quantum geometry predicts that a universe evolves through an inflationary phase at small volume before exiting gracefully into a standard Friedmann phase. This does not require the introduction of...
Isotropic Loop Quantum Cosmology (2002)
Isotropic models in loop quantum cosmology allow explicit calculations, thanks largely to a completely known volume spectrum, which is exploited in order to write down the evolution equation in a...
Poisson Geometry in Constrained Systems (2001)
Bojowald, Martin, Strobl, Thomas
Constrained Hamiltonian systems fall into the realm of presymplectic geometry. We show, however, that also Poisson geometry is of use in this context. For the case that the constraints form a closed...
The Semiclassical Limit of Loop Quantum Cosmology (2001)
The continuum and semiclassical limits of isotropic, spatially flat loop quantum cosmology are discussed, with an emphasis on the role played by the Barbero-Immirzi parameter \gamma in controlling...
The Inverse Scale Factor in Isotropic Quantum Geometry (2001)
The inverse scale factor, which in classical cosmological models diverges at the singularity, is quantized in isotropic models of loop quantum cosmology by using techniques which have been developed...
Dynamical Initial Conditions in Quantum Cosmology (2001)
Loop quantum cosmology is shown to provide both the dynamical law and initial conditions for the wave function of a universe by one discrete evolution equation. Accompanied by the condition that...
Absence of Singularity in Loop Quantum Cosmology (2001)
It is shown that the cosmological singularity in isotropic minisuperspaces is naturally removed by quantum geometry. Already at the kinematical level, this is indicated by the fact that the inverse...
Loop Quantum Cosmology III: Wheeler-DeWitt Operators (2000)
In the framework of loop quantum cosmology anomaly free quantizations of the Hamiltonian constraint for Bianchi class A, locally rotationally symmetric and isotropic models are given. Basic ideas of...
Loop Quantum Cosmology IV: Discrete Time Evolution (2000)
Using general features of recent quantizations of the Hamiltonian constraint in loop quantum gravity and loop quantum cosmology, a dynamical interpretation of the constraint equation as evolution...
Angular Momentum in Loop Quantum Gravity (2000)
An angular momentum operator in loop quantum gravity is defined using spherically symmetric states as a non-rotating reference system. It can be diagonalized simultaneously with the area operator and...
Quantum geometry and symmetry /--Martin Bojowald. (2000)
Thesis (doctoral)--Rheinisch-Westfälische Technische Hochschule Aachen, 2000.
Symplectic Cuts and Projection Quantization (1999)
Bojowald, Martin, Strobl, Thomas
The recently proposed projection quantization, which is a method to quantize particular subspaces of systems with known quantum theory, is shown to yield a genuine quantization in several cases. This...
Loop Quantum Cosmology I: Kinematics (1999)
The framework of quantum symmetry reduction is applied to loop quantum gravity with respect to transitively acting symmetry groups. This allows to test loop quantum gravity in a large class of...
Loop Quantum Cosmology II: Volume Operators (1999)
Volume operators measuring the total volume of space in a loop quantum theory of cosmological models are constructed. In the case of models with rotational symmetry an investigation of the Higgs...
Group Theoretical Quantization and the Example of a Phase Space S^1 x R^+ (1999)
Bojowald, Martin, Strobl, Thomas
The group theoretical quantization scheme is reconsidered by means of elementary systems. Already the quantization of a particle on a circle shows that the standard procedure has to be supplemented...
Abelian BF-Theory and Spherically Symmetric Electromagnetism (1999)
Three different methods to quantize the spherically symmetric sector of electromagnetism are presented: First, it is shown that this sector is equivalent to Abelian BF-theory in four spacetime...
Group Theoretical Quantization and the Example of a Phase Space S¹ × R+ (1999)
The Erwin, Schrodinger International Boltzmanngasse, Theta R, Martin Bojowald, Martin Bojowald, Thomas Strobl, ...
The group theoretical quantization scheme is reconsidered by means of elementary systems. Already the quantization of a particle on a circle shows that the standard procedure has to be supplemented...
Loop Quantum Cosmology and Boundary Proposals
Bojowald,Martin, Vandersloot,K.
For many years, the most active area of quantum cosmology has been the issue of choosing boundary conditions for the wave function of a universe. Recently, loop quantum cosmology, which is obtained...
Effective Equations of Motion for Quantum Systems
Bojowald,Martin, Skirzewski,Aureliano
In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary...
Perturbative Degrees of Freedom in Loop Quantum Gravity: Anisotropies
Bojowald,Martin, Hernandez,Hector H., Morales-Tecotl,Hugo A.
The relation between an isotropic and an anisotropic model in loop quantum cosmology is discussed in detail, comparing the strict symmetry reduction with a perturbative implementation of symmetry....
Loop Quantum Cosmology and Boundary Proposals
Bojowald, Martin, Vandersloot, K.
For many years, the most active area of quantum cosmology has been the issue of choosing boundary conditions for the wave function of a universe. Recently, loop quantum cosmology, which is obtained...