https://doi.org/10.1140/epjp/s13360-024-05074-6
Regular Article
Supervariable approach to particle on a torus knot: a model for Hodge theory
Department of Physics, National Institute of Technology Calicut, 673 601, Kozhikode, Kerala, India
Received:
26
September
2023
Accepted:
7
March
2024
Published online:
31
March
2024
We analyze a particle constrained to move on a (p, q)-torus knot within the framework of supervariable approach and deduce the BRST as well as anti-BRST symmetries. We also capture the nilpotency and absolute anti-commutativity of (anti-)BRST symmetries in this framework. Further, we show the existence of some novel symmetries in the system such as (anti-)co-BRST, bosonic, and ghost scale symmetries. We demonstrate that the conserved charges (corresponding to these symmetries) adhere to an algebra which is analogous to that of de Rham cohomological operators of differential geometry. As the charges (and the symmetries) find a physical realization with the differential geometrical operators, at the algebraic level, the present model presents a prototype for Hodge theory.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
