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

Understand

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.