Lagrangian formulation of some q-deformed systems

Abstract

In the framework of Lagrangian formulation, some q-deformed physical systems are considered. The q-deformed Legendre transformation is obtained for the free motion of a non-relativistic particle on a quantum line. This is subsequently exploited to obtain the Lagrangians for the q-deformed harmonic oscillator and q-deformed relativistic free particle. The Euler-Lagrange equations of motion are derived in a consistent manner with the corresponding Hamilton's equations. The Lagrangian for the q-deformed relativistic particle is endowed with the q-deformed gauge symmetry and reparametrization invariance which are shown to be equivalent only for $q=\pm 1$.

LaTeX, 10 pages, typos corrected, minor changes, relevant to hep-th/0302224

References in corpus (1)

• Deformed Traces and Covariant Quantum Algebras for Quantum Groups $G{L}_{qp}(2)$ and $G{L}_{qp}(1|1)$

Cited by in corpus (3)

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