Particle on a torus knot: Symplectic analysis

Abstract

We quantize a particle confined to move on a torus knot satisfying constraint condition ($p\theta +q\varphi )\approx 0$, within the context of a geometrically motivated approach - the Faddeev-Jackiw formalism. We also deduce the constraint spectrum and discern the basic brackets of the theory. We further reformulate the original gauge non-invariant theory into a physically equivalent gauge theory, which is free from any additional Wess-Zumino variables, by employing symplectic gauge invariant formalism. In addition, we analyze the reformulated gauge invariant theory within the framework of BRST formalism to establish the off-shell nilpotent and absolutely anti-commuting (anti-)BRST symmetries. Finally, we construct the conserved (anti-)BRST charges which satisfy the physicality criteria and turn out to be the generators of corresponding symmetries.

LaTeX file, 21 pages, title changed, text modified, preprint version, to appear in EPJ Plus

References in corpus (5)

• Conversion of second class constraints by deformation of Lagrangian local symmetries
• The Classical and Quantum Mechanics of a Particle on a Knot
• Free Abelian 2-Form Gauge Theory: BRST Approach
• Faddeev-Jackiw quantization of four dimensional BF theory
• Symplectic gauge invariant reformulation of a free particle system on toric geometry

Cited by in corpus (4)

• On the Quantization of FLPR Model
• Faddeev-Jackiw Approach to Classical Constrained Systems
• Barcelos-Wotzasek symplectic algorithm for constrained systems revisited
• Supervariable approach to particle on a torus knot: A model for Hodge theory