Geodesic
Wong's Equations and Charged Relativistic Particles in Non-Commutative Space
Symmetry, integrability and geometry: methods and applications, Tome 10 (2014) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: non-commutative geometry; gauge field theories; Lagrangian and Hamiltonian formalism; symmetries and conservation laws. 
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     title = {Wong's {Equations} and {Charged} {Relativistic} {Particles} {in~Non-Commutative} {Space}},
     journal = {Symmetry, integrability and geometry: methods and applications},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2014_10_a98/}
}
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Herbert Balasin; Daniel N. Blaschke; François Gieres; Manfred Schweda. Wong's Equations and Charged Relativistic Particles in Non-Commutative Space. Symmetry, integrability and geometry: methods and applications, Tome 10 (2014). http://geodesic.mathdoc.fr/item/SIGMA_2014_10_a98/

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