Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 10 (2014), 099, 21 pages      arXiv:1403.0255
Contribution to the Special Issue on Deformations of Space-Time and its Symmetries

Wong's Equations and Charged Relativistic Particles in Non-Commutative Space

Herbert Balasin a, Daniel N. Blaschke b, François Gieres c and Manfred Schweda a
a) Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstraße 8-10, A-1040 Vienna, Austria
b) Los Alamos National Laboratory, Theory Division, Los Alamos, NM, 87545, USA
c) Université de Lyon, Université Claude Bernard Lyon 1 and CNRS/IN2P3, Institut de Physique Nucléaire, Bat. P. Dirac, 4 rue Enrico Fermi, F-69622-Villeurbanne, France

Received March 02, 2014, in final form October 17, 2014; Published online October 24, 2014

In analogy to Wong's equations describing the motion of a charged relativistic point particle in the presence of an external Yang-Mills field, we discuss the motion of such a particle in non-commutative space subject to an external $U_\star(1)$ gauge field. We conclude that the latter equations are only consistent in the case of a constant field strength. This formulation, which is based on an action written in Moyal space, provides a coarser level of description than full QED on non-commutative space. The results are compared with those obtained from the different Hamiltonian approaches. Furthermore, a continuum version for Wong's equations and for the motion of a particle in non-commutative space is derived.

Key words: non-commutative geometry; gauge field theories; Lagrangian and Hamiltonian formalism; symmetries and conservation laws.

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