Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-05-05
Int.J.Mod.Phys.A22:1053-1076,2007
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX file, 23 pages, journal reference is given
Scientific paper
10.1142/S0217751X07034325
We discuss the symmetry properties of the reparametrization invariant model of an interacting relativistic particle where the electromagnetic field is taken as the constant background field. The direct coupling between the relativistic particle and the electromagnetic {\it gauge} field is a special case of the above with a specific set of subtleties involved in it. For the above model, we demonstrate the existence of a time-space noncommutativity (NC) in the spacetime structure from the symmetry considerations alone. We further show that the NC and commutativity properties of this model are different aspects of a unique continuous {\it gauge} symmetry that is derived from the non-standard gauge-type symmetry transformations by requiring their consistency with (i) the equations of motion, and (ii) the expressions for the canonical momenta, derived from the Lagrangians. We provide a detailed discussion on the noncommutative deformation of the Poincar{\'e} algebra.
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