Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-07-20
J.Phys. A37 (2004) 12077-12092
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX file, 19 pages
Scientific paper
10.1088/0305-4470/37/50/010
We show the existence of a noncommutative spacetime structure in the context of a complete discussion on the underlying spacetime symmetries for the physical system of a free massless relativistic particle. The above spacetime symmetry transformations are discussed for the first-order Lagrangian of the system where the transformations on the coordinates, velocities and momenta play very important roles. We discuss the dynamics of this system in a systematic manner by exploiting the symplectic structures associated with the four dimensional (non-)commutative cotangent (i.e. momentum phase) space corresponding to a two dimensional (non-)commutative configuration (i.e. target) space. A simple connection of the above noncommutativity (NC) is established with the NC associated with the subject of quantum groups where $SL_{q,q^{-1}} (2)$ transformations play a decisive role.
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