Are Black Hole Starships Possible (2009)
Crane, Louis, Westmoreland, Shawn
We investigate whether it is physically possible to build starships or power sources using the Hawking radiation of an artificial black hole as a power source. The proposal seems to be at the edge of...
Model Categories and Quantum Gravity (2008)
We propose a mathematically concrete way of modelling the suggestion that in quantum gravity the spacetime disappears, replacing it with a discrete approximation to the causal path space described as...
A Pointless Model for the Continuum as the Foundation for Quantum Gravity (2008)
In this paper, we outline a new approach to quantum gravity; describing states for a bounded region of spacetime as eigenstates for two classes of physically plausible gedanken experiments. We end up...
What is the Mathematical Structure of Quantum Spacetime? (2007)
We survey indications from different branches of Physics that the fine scale structure of spacetime is not adequately described by a manifold. Based on the hints we accumulate, we propose a new...
Categorical Geometry and the Mathematical Foundations of Quantum General Relativity (2006)
We explore the possibility of replacing point set topology by higher category theory and topos theory as the foundation for quantum general relativity. We discuss the BC model and problems of its...
CAUSAL SITES AS QUANTUM GEOMETRY (2005)
Abstract. We propose a structure called a causal site to use as a setting for quantum geometry, replacing the underlying point set. The structure has an interesting categorical form, and a natural...
Causal sites as quantum geometry (2004)
Christensen, J. Daniel, Crane, Louis
We propose a structure called a causal site to use as a setting for quantum geometry, replacing the underlying point set. The structure has an interesting categorical form, and a natural "tangent...
A More Sensitive Lorentzian State Sum (2003)
We give the construction modulo normalization of a new state sum model for lorentzian quantum general relativity, using the construction of Dirac's expansors to include quantum operators...
A New Approach to the Geometrization of Matter (2001)
We show that the sum over geometries in the Lorentzian 4-D state sum model for quantum GR in [1] includes terms which correspond to geometries on manifolds with conical singularities. Natural...
A finiteness proof for the Lorentzian state sum spinfoam model for quantum general relativity (2001)
Crane, Louis, Perez, Alejandro, Rovelli, Carlo
We show that the normalized Lorentzian state sum is finite on any triangulation. It thus provides a candidate for a perturbatively finite quantum theory of general relativity in four dimensions with...
Hypergravity and Categorical Feynmanology (2000)
We propose a new line of attack to create a finite quantum theory which includes general relativity and (perhaps) the standard model in its low energy limit. The theory would emerge from the...
A Lorentzian Signature Model for Quantum General Relativity (2000)
Barrett, John W., Crane, Louis
We give a relativistic spin network model for quantum gravity based on the Lorentz group and its q-deformation, the Quantum Lorentz Algebra. We propose a combinatorial model for the path integral...
A Lorentzian Signature Model for Quantum General Relativity (2000)
Barrett, John W., Crane, Louis
We give a relativistic spin network model for quantum gravity based on the Lorentz group and its q-deformation, the Quantum Lorentz Algebra. We propose a combinatorial model for the path integral...
A Lorentzian Signature Model for Quantum General Relativity (2000)
Barrett, John W., Crane, Louis
We give a relativistic spin network model for quantum gravity based on the Lorentz group and its q-deformation, the Quantum Lorentz Algebra. We propose a combinatorial model for the path integral...
A Lorentzian Signature Model for Quantum General Relativity (1999)
Barrett, John W., Crane, Louis
We give a relativistic spin network model for quantum gravity based on the Lorentz group and its q-deformation, the Quantum Lorentz Algebra. We propose a combinatorial model for the path integral...
An Octonionic Geometric (Balanced) state Sum Model (1998)
We propose a new 4D state sum model, related to the balanced model, which is constructed using the octonions, or equivalently, triality. An effective continuum physical theory constructed from this...
Relativistic Spin Networks and Quantum Gravity (1998)
. Relativistic spin networks are defined by considering the spin covering of the group SO(4), SU(2) \Theta SU(2). Relativistic quantum spins are related to the geometry of the 2-dimensional faces of...
On the interpretation of relativistic spin networks and the balanced state sum (1997)
We discuss the interpretation of the state sum of Barrett and Crane.
Relativistic spin networks and quantum gravity (1997)
Barrett, John W., Crane, Louis
Relativistic spin networks are defined by considering the spin covering of the group SO(4), SU(2) times SU(2). Relativistic quantum spins are related to the geometry of the 2-dimensional faces of a...
A Proposal for the Quantum Theory of Gravity (1997)
We propose a model for the quantum theory of gravity. the model has diffeomorphism invariance, a natural length scale, and (plausibly) propagating modes. in the new addendum, we alter the model in a...
Deformations of (Bi) tensor Categories (1996)
We define the cohomology and formal deformation theories for algebra and bialgebra categories. We suggest some approaches to finding nontrivial deformations of the categories associated to the...
An algebraic interpretation of the Wheeler-DeWitt equation (1996)
Barrett, John W., Crane, Louis
We make a direct connection between the construction of three dimensional topological state sums from tensor categories and three dimensional quantum gravity by noting that the discrete version of...
Examples of categorification (1996)
Crane, Louis, Yetter, David N.
We construct tensor and bitensor categories with given Grothedieck rig (fusion algebra) in simple cases. The results provide examples on which to test the conjectural construction of 4-D TQFT's...
Clock and Category; IS QUANTUM GRAVITY ALGEBRAIC (1995)
We investigate the possibility that the quantum theory of gravity could be constructed discretely using algebraic methods. The algebraic tools are similar to ones used in constructing topological...
State-Sum Invariants of 4-Manifolds I (1994)
Crane, Louis, Kauffman, Louis H., Yetter, David N.
We provide, with proofs, a complete description of the authors' construction of state-sum invariants announced in [CY], and its generalization to an arbitrary (artinian) semisimple tortile category....
Four dimensional topological quantum field theory, Hopf categories, and the canonical bases (1994)
Crane, Louis, Frenkel, Igor B.
We propose a new mwthod of constructing 4D-TQFTs. The method uses a new type of algebraic structure called a Hopf Category. We also outline the construction of a family of Hopf categories related to...
Possible Implications of the Quantum Theory of Gravity (1994)
We consider the implications of some simple assumptions about the nature of the quantum theory of gravity which are plausible for a class of possible theories I have been attempting to construct. The...
On the Classicality of Broda's SU(2) Invariant of 4-manifolds (1993)
Crane, Louis, Kauffman, Louis H., Yetter, David N.
Recent work of Roberts has shown that the first surgical 4-manifold invariant of Broda and (up to an unspecified normalization factor) the state-sum invariant arising from the TQFT of Crane-Yetter...
Evaluating the Crane-Yetter Invariant (1993)
Crane, Louis, Kauffman, Louis H., Yetter, David N.
We provide an explicit formula for the invariant of 4-manifolds introduced by Crane and Yetter (in hep-th 9301062). A consequence of our result is the existence of a combinatorial formula for the...
Topological Field Theory As The Key To Quantum Gravity (1993)
Motivated by the similarity between CSW theory and the Chern Simons state for General Relativity in the Ashtekar variables, we explore what the universe would look like if it were in a state...
We Are Not Stuck With Gluing (1993)
Yetter, David N., Crane, Louis
We show that the construction of Ocneanu, which yields 1 for any 4D manifold, is not identical to our construction, which gives different numbers for different manifolds.
I propose a new mathematical form for the quantum theory of gravity coupled to matter. The motivation is from the connection between CSW TQFT and the Ashtekar variables. I also connect the algebraic...
A categorical construction of 4D TQFTs (1993)
Crane, Louis, Yetter, David N.
We construct a four dimensional topological Quantum Field Theory from a modular tensor category. We complete the proof in the case of SU(2)q at a root of unity. Our construction may be important in...