Nonrelativistic conformal structures
The ``Kaluza-Klein-type'' geometric structure appropriate to study the central extension of the Galilei group and non-relativistic physics is reviewed.
math-ph↗
arXiv subjects
P. A. Horvathy
Publications and source records attributed to P. A. Horvathy.
Mathisson' spinning electron: noncommutative mechanics & exotic Galilean symmetry, 66 years ago
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 classical electron [Acta Physica Polonica 6, 218 (1937)], further discussed by Weyssenhoff and Raabe [Acta Physica Polonica 9, 7 (1947)]. The two-parameter centrally extended Galilean symmetry of the model is recoved using elementary methods. The relation to Schrödinger's Zitternde Elektron is indicated.
hep-th↗
Galilean symmetry in noncommutative field theory
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 boosts, but also the two-fold centrally extended ``exotic'' Galilean symmetry, where the commutator of the boosts yields the noncommutative parameter. In the free case, one gets an ``exotic'' two-parameter central extension of the Schroedinger group. The conformal symmetry is, however, broken by the interaction.
hep-th↗
The non-commutative Landau problem
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 all Landau levels. The ``exotic'' approach, where the coupling to the gauge field is achieved using the symplectic structure, only yields lowest-Landau level states, as advocated by Peierls and used in the description of the ground states of the Fractional Quantum Hall Effect. The same reduced model also describes vortex dynamics in a superfluid ${}^4$He film. Remarkably, the spectrum depends crucially on the quantization scheme. The system is symmetric w. r. t. area-preserving diffeomorphisms.
hep-th↗
Spin and exotic Galilean symmetry
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 of the Galilei group, with independent spin and exotic structure.
hep-th↗
Exotic galilean symmetry and the Hall effect
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 magnetic field of critical strength determined by the extension parameters, the system becomes singular, and ``Faddeev-Jackiw'' reduction yields the ``Chern-Simons'' mechanics of Dunne, Jackiw, and Trugenberger. The reduced system moves according to the Hall law.
hep-th↗
Bäcklund transformation for non-relativistic Chern-Simons vortices
A Bäcklund transformation yielding the static non-relativistic Chern-Simons vortices of Jackiw and Pi is presented.
hep-th↗
Conformal Properties of Chern-Simons Vortices in External Fields
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 non-relativistic Kaluza-Klein-type framework presented in our previous paper. All Schrodinger-symmetric backgrounds are determined.
hep-ph↗
Conformal symmetry of the coupled Chern-Simons and gauged nonlinear Schrödinger equations
The non-relativistic conformal symmetry found by Jackiw and Pi for the coupled Chern-Simons and gauged nonlinear Schrödinger equations in the plane is derived in a non-relativistic Kaluza-Klein framework.
hep-th↗