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

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2014
• Main Authors: Balasin, H., Blaschke, D.N., Gieres, F., Schweda, M.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2014
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/146542
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Wong's Equations and Charged Relativistic Particles in Non-Commutative Space / H. Balasin, D.N. Blaschke, F. Gieres, M. Schweda // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 45 назв. — англ.

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⋆(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.