arXiv subjects

Anjali S

Publications and source records attributed to Anjali S.

6 recordsLinked to original sources

arXiv2023

Supervariable approach to particle on a torus knot: A model for Hodge theory

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.

hep-th↗

arXiv2022

Particle on a torus knot: Symplectic analysis

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

hep-th↗

arXiv2021

Symplectic gauge invariant reformulation of a free particle system on toric geometry

We deduce the constraint structure and subsequently quantize a free particle system residing on a torus satisfying the geometric constraint $(r-a)=0$, within the framework of modified Faddeev-Jackiw formalism. Further, we reformulate the system as a gauge theory by the means of symplectic gauge invariant formalism. Finally, we establish the off-shell nilpotent and absolutely anti-commuting (anti-)BRST symmetries of the reformulated gauge invariant theory.

hep-th↗

arXiv2020

Coupled $\mathcal{N}$ = 2 supersymmetric quantum systems: symmetries and supervariable approach

We consider specific examples of $\mathcal{N}$ = 2 supersymmetric quantum mechanical models and list out all the novel symmetries. In each case, we show the existence of two sets of discrete symmetries that correspond to the Hodge duality operator of differential geometry. Thus, we are able to provide a proof of the conjecture which endorses the existence of more than one discrete symmetry transformation as the analogue of Hodge duality operation. Finally, we extend our analysis to a more general case and derive on-shell nilpotent symmetries within the framework of supervariable approach.

hep-th↗

arXiv2020

Revisiting Novel Symmetries in Coupled $\mathcal{N} = 2$ Supersymmetric Quantum Systems: Examples and Supervariable Approach

We revisit the novel symmetries in $\mathcal{N}$ = 2 supersymmetric (SUSY) quantum mechanical (QM) models by considering specific examples of coupled systems. Further, we extend our analysis to a general case and list out all the novel symmetries. In each case, we show the existence of two sets of discrete symmetries that correspond to the Hodge duality operator of differential geometry. Thus, we are able to provide a proof of the conjecture which points out the existence of more than one set of discrete symmetry transformations corresponding to the Hodge duality operator. Moreover, we derive on-shell nilpotent symmetries for a generalized superpotential within the framework of supervariable approach.

hep-th↗

arXiv2019

Faddeev-Jackiw Quantization of Christ-Lee Model

We analyze the constraints of Christ-Lee model by the means of modified Faddeev-Jackiw formalism in Cartesian as well as polar coordinates. Further, we accomplish quantization à la Faddeev-Jackiw by choosing appropriate gauge conditions in both the coordinate systems. Finally, we establish gauge symmetries of Christ-Lee model with the help of zero modes of the symplectic matrix.

hep-th↗