QUANTIZATION OF A $q$-DEFORMED FREE RELATIVISTIC PARTICLE

Abstract

A $q$-deformed free scalar relativistic particle is discussed in the framework of the BRST formalism. The $q$-deformed local gauge symmetry and reparametrization invariance of the first-order Lagrangian have been exploited for the BRST quantization of this system on a $G{L}_q(2)$ invariant quantum world-line. The on-shell equivalence of these BRST charges requires the deformation parameter to be $\pm 1$ under certain identifications.The same restriction ($q=\pm 1$) emerges from the conservation of the $q$-deformed BRST charge on an arbitrary (unconstrained) manifold and the validity of the BRST algebra. The solutions for the equations of motion respect $G{L}_q(2)$ invariance on the mass-shell at any arbitrary value of the evolution parameter characterizing the quantum world-line.

LATEX, 12 pages

Cited by in corpus (4)

• Noncommutativity In The Mechanics Of A Free Massless Relativistic Particle
• Interacting Relativistic Particle: Time-Space Noncommutativity And Symmetries
• Quantum deformation of cubic string field theory
• Cohomological Operators and Covariant Quantum Superalgebras