On $q$-Deformed Spinning Relativistic Particle

Abstract

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 $q=\pm 1$ under particular identification of the transformation parameters. The same condition ($q=\pm 1$) 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 $G{L}_{\surd q}(1|1)$ and $G{L}_q(2)$ invariances for any arbitrary value of the evolution parameter characterizing the quantum super world-line.

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

References in corpus (4)

• Exactly Solvable Potentials and Quantum Algebras
• Quantum Group Gauge Theories and Covariant Quantum Algebras
• Deformed Traces and Covariant Quantum Algebras for Quantum Groups $G{L}_{qp}(2)$ and $G{L}_{qp}(1|1)$
• Lagrangian formulation of some q-deformed systems

Cited by in corpus (4)

• Lagrangian Models of the Particles with Spin: The First Seventy Years
• Noncommutativity In The Mechanics Of A Free Massless Relativistic Particle
• Interacting Relativistic Particle: Time-Space Noncommutativity And Symmetries
• Cohomological Operators and Covariant Quantum Superalgebras