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arXiv · hep-th/0407167

Noncommutativity In The Mechanics Of A Free Massless Relativistic Particle

R. P. Malik
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Abstract

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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R. P. Malik. 2004-12-03. Noncommutativity In The Mechanics Of A Free Massless Relativistic Particle. https://doi.org/10.1088/0305-4470%2F37%2F50%2F010

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