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arXiv · 2108.08788

Particle on a torus knot: Symplectic analysis

Anjali S·Saurabh Gupta
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Abstract

We quantize a particle confined to move on a torus knot satisfying constraint condition ($p \theta + q \phi) \approx 0$, 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.

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Anjali S, Saurabh Gupta. 2021-08-19. Particle on a torus knot: Symplectic analysis. https://doi.org/10.1140/epjp%2Fs13360-022-02699-3

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