On $q$-Deformed Spinning Relativistic Particle

Details On $q$-Deformed Spinning Relativistic Particle On $q$-Deformed Spinning Relativistic Particle

1994-10-23

arxiv.org/abs/hep-th/9410173v1

Phys. Lett. B345 (1995) 131-138

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, Preprint JINR E2-94-410, LaTeX file

Scientific paper

10.1016/0370-2693(94)01588-4

A $q$-deformed free spinning relativistic particle is discussed in the framework of the Lagrangian formalism. Three equivalent Lagrangians are obtained for this system which are endowed with $q$-deformed local (super)gauge symmetries and reparametrization invariance. It is demonstrated that these symmetries are on-shell equivalent only for $ q = \pm1 $ under particular identification of the transformation parameters. The same condition ($ q=\pm1 $) emerges due to the requirement that the $q$-commutator of two supersymmetric gauge transformations should generate a reparametrization plus a supersymmetric gauge transformation. For a specific gauge choice, the solutions for equations of motion respect $GL_{\surd q}(1|1)$ and $GL_{q}(2)$ invariances for any arbitrary value of the evolution parameter characterizing the quantum super world-line.

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