QUANTIZATION OF A $q$-DEFORMED FREE RELATIVISTIC PARTICLE

Details QUANTIZATION OF A $q$-DEFORMED FREE RELATIVISTIC PARTICLE QUANTIZATION OF A $q$-DEFORMED FREE RELATIVISTIC PARTICLE

1995-03-04

arxiv.org/abs/hep-th/9503025v1

Mod.Phys.Lett. A11 (1996) 2871-2881

Physics

High Energy Physics

High Energy Physics - Theory

LATEX, 12 pages

Scientific paper

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 $GL_{q}(2)$ 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 $GL_{q}(2)$ invariance on the mass-shell at any arbitrary value of the evolution parameter characterizing the quantum world-line.

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