The geometry of Schr\"odinger symmetry in non-relativistic CFT (2008)
Duval, C., Hassaine, M., Horvathy, P. A.
The non-relativistic conformal "Schr\"odinger" symmetry of some gravity backgrounds proposed recently in the AdS/CFT context, is explained in the "Bargmann framework". The formalism incorporates the...
Non-Relativistic Conformal and Supersymmetries (2008)
Non-relativistic conformal (''Schr\"odinger'') symmetry is derived in a Kaluza-Klein type framework. Lightlike reduction of the massless Dirac equation from 5D Minkowski space yields L\'evy-Leblond's...
Lectures on (abelian) Chern-Simons vortices (2007)
Various aspects including the construction and the symmetries of Abelian Chern-Simons vortices are reviewed. Extended version of the Lectures delivered at NIKHEF (Amsterdam), July 2006. Typos...
Berry phase correction to electron density in solids and "exotic" dynamics (2007)
Duval, C., Horvath, Z., Horvathy, P. A., Martina, L., Stichel, P.
Recent results on the semiclassical dynamics of an electron in a solid are explained using techniques developed for ``exotic'' Galilean dynamics. The system is indeed Hamiltonian and Liouville's...
The Maslov correction in the semiclassical Feynman integral (2007)
The Maslov correction to the wave function is to the jump of $-\pi/2$ in the phase when the system passes through a caustic point. This phenomenon is related to the second variation and to the...
Fermat Principle for spinning light (2007)
Duval, C., Horvathy, Z., Horvathy, P. A.
Mimicking the description of spinning particles in General Relativity, the Fermat Principle is extended to spinning photons. Linearization of the resulting Papapetrou-Souriau type equations yields...
Dynamics of semiclassical Bloch wave - packets (2006)
The semiclassical approximation for electron wave-packets in crystals leads to equations which can be derived from a Lagrangian or, under suitable regularity conditions, in a Hamiltonian framework....
Non-commutative mechanics, in mathematical & in condensed matter physics (2006)
Non-commutative structures were introduced, independently and around the same time, in mathematical and in condensed matter physics (see Table~1). Souriau's construction applied to the two-parameter...
Anomalous Hall Effect in non-commutative mechanics (2006)
The anomalous velocity term in the semiclassical model of a Bloch electron deviates the trajectory from the conventional one. When the Berry curvature (alias noncommutative parameter) is a monopole...
The ``exotic'' particle model with non-commuting position coordinates, associated with the two-parameter central extension of the planar Galilei group, can be used to derive the ground states of the...
Strings in plane-fronted gravitational waves (2006)
Duval, C., Horvath, Z., Horvathy, P. A.
Brinkmann's plane-fronted gravitational waves with parallel rays --~shortly pp-waves~-- are shown to provide, under suitable conditions, exact string vacua at all orders of the sigma-model...
The Biedenharn Approach to Relativistic Coulomb-type Problems (2006)
The approach developped by Biedeharn in the sixties for the relativistic Coulomb problem is reviewed and applied to various physical problems.
Dynamal (super)symmetries of monopoles and vortices (2005)
The dynamical (super)symmetries for various monopole systems are reviewed. For a Dirac monopole, no smooth Runge-Lenz vector can exist; there is, however, a spectrum-generating conformal $o(2,1)$...
Helicity supersymmetry of dyons (2005)
The 'dyon' system of D'Hoker and Vinet consisting of a spin 1/2 particle with anomalous gyromagnetic ratio 4 in the combined field of a Dirac monopole plus a Coulomb plus a suitable $1/r^2$ potential...
Non-relativistic supersymmetry (2005)
The supersymmetric extensions of the Schr\"odinger algebra are reviewed.
The Dirac equation in Taub-NUT space (2005)
Using chiral supersymmetry, we show that the massless Dirac equation in the Taub-NUT gravitational instanton field is exactly soluble and explain the arisal and the use of the dynamical (super)...
Hamiltonian aspects of Bogoliubov quasiparticles (2005)
Horvath, Z., Horvathy, P. A., Martina, L.
The Bogoliubov particle considered in [cond-mat/0507125] admits, contrarily to the claim of the authors, an interesting Hamiltonian structure.
Fermat Principle for spinning light (2005)
Duval, C., Horvathy, Z., Horvathy, P. A.
Mimicking the description of spinning particles in General Relativity, the Fermat Principle is extended to spinning photons. Linearization of the resulting Papapetrou-Souriau type equations yields...
On Schr\"odinger superalgebras (2005)
We construct, using the supersymplectic framework of Berezin, Kostant and others, two types of supersymmetric extensions of the Schr\"odinger algebra (itself a conformal extension of the Galilei...
Enlarged Galilean symmetry of anyons and the Hall effect (2005)
Horvathy, P. A., Martina, L., Stichel, P.
Enlarged planar Galilean symmetry, built of both space-time and field variables and also incorporating the ``exotic\'\' central extension is introduced. It is used to describe non-relativistic anyons...
Comments on spin-orbit interaction of anyons (2005)
Horvathy, P A, Martina, L., Stichel, P.
The coupling of non-relativistic anyons (called exotic particles) to an electromagnetic field is considered. Anomalous coupling is introduced by adding a spin-orbit term to the Lagrangian....
Anyons with anomalous gyromagnetic ratio & the Hall effect (2005)
Letting the mass depend on the spin-field coupling as $M^2=m^2-(eg/2c^2)F_{\\alpha\\beta}S^{\\alpha\\beta}$, we propose a new set of relativistic planar equations of motion for spinning anyons. Our...
The acceleration-dependent system with noncommuting coordinates, proposed by Lukierski, Stichel and Zakrzewski [Ann. Phys. 260, 224 (1997)] is derived as the non-relativistic limit of Mathisson's...
Galilean symmetry in noncommutative field theory (2005)
Horvathy, P. A., Martina, L., Stichel, P. C.
When the interaction potential is suitably reordered, the Moyal field theory admits two types of Galilean symmetries, namely the conventional mass-parameter-centrally-extended one with commuting...
Galilean noncommutative gauge theory: symmetries & vortices (2005)
Horvathy, P. A., Martina, L., Stichel, P. C.
Noncommutative Chern-Simons gauge theory coupled to nonrelativistic scalars or spinors is shown to admit the ``exotic\'\' two-parameter-centrally extended Galilean symmetry, realized in a unique way...
Moving vortices in noncommutative gauge theory (2005)
Horvathy, P. A., Stichel, P. C.
Exact time-dependent solutions of nonrelativistic noncommutative Chern - Simons gauge theory are presented in closed analytic form. They are different from (indeed orthogonal to) those discussed...
Spin and exotic Galilean symmetry (2005)
A slightly modified and regularized version of the non-relativistic limit of the relativistic anyon model considered by Jackiw and Nair yields particles associated with the twofold central extension...
The non-commutative Landau problem (2005)
The Landau problem is discussed in two similar but still different non-commutative frameworks. The ``standard\'\' one, where the coupling to the gauge field is achieved using Poisson brackets, yields...
Exotic galilean symmetry and the Hall effect (2005)
The ``Laughlin\'\' picture of the Fractional Quantum Hall effect can be derived using the ``exotic\'\' model based on the two-fold centrally-extended planar Galilei group. When coupled to a planar...
Berry phase correction to electron density in solids and "exotic" dynamics (2005)
Duval, C., Horvath, Z., Horvathy, P. A., Martina, L., Stichel, P.
Recent results on the semiclassical dynamics of an electron in a solid are explained using techniques developed for ``exotic'' Galilean dynamics. The system is indeed Hamiltonian and Liouville's...
Comments on spin-orbit interaction of anyons (2005)
Horvathy, P A, Martina, L., Stichel, P.
The coupling of non-relativistic anyons (called exotic particles) to an electromagnetic field is considered. Anomalous coupling is introduced by adding a spin-orbit term to the Lagrangian....
Enlarged Galilean symmetry of anyons and the Hall effect (2005)
Horvathy, P. A., Martina, L., Stichel, P.
Enlarged planar Galilean symmetry, built of both space-time and field variables and also incorporating the ``exotic\'\' central extension is introduced. It is used to describe non-relativistic anyons...
Comments on spin-orbit interaction of anyons (2005)
Horvathy, P A, Martina, L., Stichel, P.
The coupling of non-relativistic anyons (called exotic particles) to an electromagnetic field is considered. Anomalous coupling is introduced by adding a spin-orbit term to the Lagrangian....
Enlarged Galilean symmetry of anyons and the Hall effect (2005)
Horvathy, P. A., Martina, L., Stichel, P.
Enlarged planar Galilean symmetry, built of both space-time and field variables and also incorporating the ``exotic\'\' central extension is introduced. It is used to describe non-relativistic anyons...
Comments on spin-orbit interaction of anyons (2005)
Horvathy, P A, Martina, L., Stichel, P.
The coupling of non-relativistic anyons (called exotic particles) to an electromagnetic field is considered. Anomalous coupling is introduced by adding a spin-orbit term to the Lagrangian....
Enlarged Galilean symmetry of anyons and the Hall effect (2004)
Horvathy, P. A., Martina, L., Stichel, P.
Enlarged planar Galilean symmetry, built of both space-time and field variables and also incorporating the ``exotic'' central extension is introduced. It is used to describe non-relativistic anyons...
Symmetries of field theories on the non-commutative plane (2004)
Horvathy, P. A., Martina, L., Stichel, P. C.
New developments on the symmetries of non-relativistic field theoretical models on the non commutative plane are reviewed. It is shown in particular that Galilean invariance strongly restricts the...
Edge solitons in the QHE (2004)
Hassaine, M, Horvathy, P. A., Yera, J-C.
The spacelike reduction of the Chern-Simons Lagrangian yields a modified Nonlinear Schr\"odinger Equation (jNLS) where in the non-linearity the particle density is replaced by current. When the phase...
New applications of the Biedenharn-Temple operator (2004)
The Biedenharn approach to the Dirac-Coulomb problem is applied to a system considered by D'Hoker and Vinet, which consists of a spin $\2$ particle in the combined field of a Dirac monopole plus a...
Non-commuting coordinates, exotic particles, & anomalous anyons in the Hall effect (2004)
Our previous ``exotic'' particle, together with the more recent anomalous anyon model (which has arbitrary gyromagnetic factor $g$) are reviewed. The non-relativistic limit of the anyon generalizes...
Anyons with anomalous gyromagnetic ratio & the Hall effect (2004)
Letting the mass depend on the spin-field coupling as $M^2=m^2-(eg/2c^2)F_{\alpha\beta}S^{\alpha\beta}$, we propose a new set of relativistic planar equations of motion for spinning anyons. Our model...
Anyons with anomalous gyromagnetic ratio & the Hall effect (2004)
Letting the mass depend on the spin-field coupling as $M^2=m^2-(eg/2c^2)F_{\\alpha\\beta}S^{\\alpha\\beta}$, we propose a new set of relativistic planar equations of motion for spinning anyons. Our...
Anyons with anomalous gyromagnetic ratio & the Hall effect (2004)
Letting the mass depend on the spin-field coupling as $M^2=m^2-(eg/2c^2)F_{\\alpha\\beta}S^{\\alpha\\beta}$, we propose a new set of relativistic planar equations of motion for spinning anyons. Our...
Moving vortices in noncommutative gauge theory (2003)
Horvathy, P. A., Stichel, P. C.
Exact time-dependent solutions of nonrelativistic noncommutative Chern - Simons gauge theory are presented in closed analytic form. They are different from (indeed orthogonal to) those discussed...
Celestial mechanics, from high-school to Newton's Principia (2003)
A high-school exercise is used to get an insight into planetary motion.
Noncommuting coordinates in the Hall effect and in vortex dynamics (2003)
Laughlin's Ansatz to explain the fractional Quantum Hall effect is derived by coupling a particle associated with ``exotic'' the two-fold central extension of the planar Galilei group. The reduced...
In (2+1) dimensions, the Maxwell term $-(1/4) F_{\alpha\beta}F^{\alpha\beta}$ can be replaced by the Chern-Simons three-form $(\kappa/4)\epsilon^{\alpha\beta\gamma}A_\alpha F_{\beta\gamma}$, yielding...
Galilean noncommutative gauge theory: symmetries & vortices (2003)
Horvathy, P. A., Martina, L., Stichel, P. C.
Noncommutative Chern-Simons gauge theory coupled to nonrelativistic scalars or spinors is shown to admit the ``exotic'' two-parameter-centrally extended Galilean symmetry, realized in a unique way...
Vanishing of the conformal anomaly for strings in a gravitational wave (2003)
Duval, C., Horvath, Z., Horvathy, P. A.
Using the non-symmetric-connection approach proposed by Osborn, we demonstrate that, for a bosonic string in a specially chosen plane-fronted gravitational wave and an axion background, the conformal...
Nonrelativistic conformal structures (2003)
The ``Kaluza-Klein-type'' geometric structure appropriate to study the central extension of the Galilei group and non-relativistic physics is reviewed.
Galilean symmetry in noncommutative field theory (2003)
Horvathy, P. A., Martina, L., Stichel, P. C.
When the interaction potential is suitably reordered, the Moyal field theory admits two types of Galilean symmetries, namely the conventional mass-parameter-centrally-extended one with commuting...
The acceleration-dependent system with noncommuting coordinates, proposed by Lukierski, Stichel and Zakrzewski [Ann. Phys. 260, 224 (1997)] is derived as the non-relativistic limit of Mathisson's...
The acceleration-dependent system with noncommuting coordinates, proposed by Lukierski, Stichel and Zakrzewski [Ann. Phys. 260, 224 (1997)] is derived as the non-relativistic limit of Mathisson's...
Galilean symmetry in noncommutative field theory (2003)
Horvathy, P. A., Martina, L., Stichel, P. C.
When the interaction potential is suitably reordered, the Moyal field theory admits two types of Galilean symmetries, namely the conventional mass-parameter-centrally-extended one with commuting...
Galilean noncommutative gauge theory: symmetries & vortices (2003)
Horvathy, P. A., Martina, L., Stichel, P. C.
Noncommutative Chern-Simons gauge theory coupled to nonrelativistic scalars or spinors is shown to admit the ``exotic\'\' two-parameter-centrally extended Galilean symmetry, realized in a unique way...
Moving vortices in noncommutative gauge theory (2003)
Horvathy, P. A., Stichel, P. C.
Exact time-dependent solutions of nonrelativistic noncommutative Chern - Simons gauge theory are presented in closed analytic form. They are different from (indeed orthogonal to) those discussed...
The acceleration-dependent system with noncommuting coordinates, proposed by Lukierski, Stichel and Zakrzewski [Ann. Phys. 260, 224 (1997)] is derived as the non-relativistic limit of Mathisson's...
Galilean symmetry in noncommutative field theory (2003)
Horvathy, P. A., Martina, L., Stichel, P. C.
When the interaction potential is suitably reordered, the Moyal field theory admits two types of Galilean symmetries, namely the conventional mass-parameter-centrally-extended one with commuting...
Galilean noncommutative gauge theory: symmetries & vortices (2003)
Horvathy, P. A., Martina, L., Stichel, P. C.
Noncommutative Chern-Simons gauge theory coupled to nonrelativistic scalars or spinors is shown to admit the ``exotic\'\' two-parameter-centrally extended Galilean symmetry, realized in a unique way...
Moving vortices in noncommutative gauge theory (2003)
Horvathy, P. A., Stichel, P. C.
Exact time-dependent solutions of nonrelativistic noncommutative Chern - Simons gauge theory are presented in closed analytic form. They are different from (indeed orthogonal to) those discussed...
Spin and exotic Galilean symmetry (2002)
A slightly modified and regularized version of the non-relativistic limit of the relativistic anyon model considered by Jackiw and Nair yields particles associated with the twofold central extension...
Exotic galilean symmetry in non-commutative field theory (2002)
The non-relativistic version of the non commutative Field Theory, recently introduced by Lozano, Moreno and Schaposnik [1], is shown to admit the ``exotic'' Galilean symmetry found before for point...
The non-commutative Landau problem (2002)
The Landau problem is discussed in two similar but still different non-commutative frameworks. The ``standard'' one, where the coupling to the gauge field is achieved using Poisson brackets, yields...
Spin and exotic Galilean symmetry (2002)
A slightly modified and regularized version of the non-relativistic limit of the relativistic anyon model considered by Jackiw and Nair yields particles associated with the twofold central extension...
The non-commutative Landau problem (2002)
The Landau problem is discussed in two similar but still different non-commutative frameworks. The ``standard\'\' one, where the coupling to the gauge field is achieved using Poisson brackets, yields...
Spin and exotic Galilean symmetry (2002)
A slightly modified and regularized version of the non-relativistic limit of the relativistic anyon model considered by Jackiw and Nair yields particles associated with the twofold central extension...
The non-commutative Landau problem (2002)
The Landau problem is discussed in two similar but still different non-commutative frameworks. The ``standard\'\' one, where the coupling to the gauge field is achieved using Poisson brackets, yields...
Exotic galilean symmetry and the Hall effect (2001)
The ``Laughlin'' picture of the Fractional Quantum Hall effect can be derived using the ``exotic'' model based on the two-fold centrally-extended planar Galilei group. When coupled to a planar...
Exotic galilean symmetry and the Hall effect (2001)
The ``Laughlin\'\' picture of the Fractional Quantum Hall effect can be derived using the ``exotic\'\' model based on the two-fold centrally-extended planar Galilei group. When coupled to a planar...
Exotic galilean symmetry and the Hall effect (2001)
The ``Laughlin\'\' picture of the Fractional Quantum Hall effect can be derived using the ``exotic\'\' model based on the two-fold centrally-extended planar Galilei group. When coupled to a planar...
B\"acklund transformation for non-relativistic Chern-Simons vortices (1996)
A B\"acklund transformation yielding the static non-relativistic Chern-Simons vortices of Jackiw and Pi is presented.
Conformal Properties of Chern-Simons Vortices in External Fields (1994)
Duval, C., Horvathy, P. A., Palla, L.
The construction and the symmetries of Chern-Simons vortices in harmonic and uniform magnetic force backgrounds found by Ezawa, Hotta and Iwazaki, and by Jackiw and Pi are generalized using the...
Conformal symmetry of the coupled Chern-Simons and gauged nonlinear Schr\"odinger equations (1994)
Duval, C., Horvathy, P. A., Palla, L.
The non-relativistic conformal symmetry found by Jackiw and Pi for the coupled Chern-Simons and gauged nonlinear Schr\"odinger equations in the plane is derived in a non-relativistic Kaluza-Klein...