Noncommutativity In The Mechanics Of A Free Massless Relativistic Particle

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 $S{L}_{q,q^{-1}}(2)$ transformations play a decisive role.

arXiv commentLaTeX file, 19 pages

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Cited by in corpus (6)

• Noncommutative spaces, the quantum of time and the Lorentz symmetry
• Time-Space Noncommutativity And Symmetries For A Massive Relativistic Particle
• Massive Spinning Relativistic Particle: Revisited Under BRST and Supervariable Approaches
• Interacting Relativistic Particle: Time-Space Noncommutativity And Symmetries
• Extended Conformal Algebra and Non-commutative Geometry in Particle Theory
• Noncommutativity In A Simple Toy Model