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

Abstract

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.

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Cited by in corpus (7)

• The Energy-Momentum Tensor(s) in Classical Gauge Theories
• Chiral fermions as classical massless spinning particles
• On the energy-momentum tensor in Moyal space
• Noether's theorems and conserved currents in gauge theories in the presence of fixed fields
• Aspects of perturbative quantum field theory on non-commutative spaces
• Emergent spacetime from a Berry-inspired dynamical gauge field coupled to electromagnetism
• Noncommutative Classical Dynamics on Velocity Phase Space and Souriau Formalism