Research Article Massive Spinning Relativistic Particle: Revisited under BRST and Supervariable Approaches A. Tripathi , 1 B. Chauhan , 1 A. K. Rao, 1 and R. P. Malik 1,2 1 Physics Department, Institute of Science, Banaras Hindu University, Varanasi 221 005, India 2 DST Centre for Interdisciplinary Mathematical Sciences, Institute of Science, Banaras Hindu University, Varanasi 221 005, India Correspondence should be addressed to R. P. Malik; rpmalik1995@gmail.com Received 1 July 2020; Accepted 29 July 2020; Published 17 August 2020 Academic Editor: Sunny Vagnozzi Copyright © 2020 A. Tripathi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP 3 . We discuss the continuous and infinitesimal gauge, supergauge, reparameterization, nilpotent Becchi-Rouet-Stora-Tyutin (BRST), and anti-BRST symmetries and derive corresponding nilpotent charges for the one ð0+1Þ-dimensional (1D) massive model of a spinning relativistic particle. We exploit the theoretical potential and power of the BRST and supervariable approaches to derive the (anti-)BRST symmetries and coupled (but equivalent) Lagrangians for this system. In particular, we capture the off-shell nilpotency and absolute anticommutativity of the conserved (anti-)BRST charges within the framework of the newly proposed (anti-)chiral supervariable approach (ACSA) to BRST formalism where only the (anti-)chiral supervariables (and their suitable super expansions) are taken into account along the Grassmannian direction(s). One of the novel observations of our present investigation is the derivation of the Curci-Ferrari- (CF-) type restriction by the requirement of the absolute anticommutativity of the (anti-)BRST charges in the ordinary space. We obtain the same restriction within the framework of ACSA to BRST formalism by (i) the symmetry invariance of the coupled Lagrangians and (ii) the proof of the absolute anticommutativity of the conserved and nilpotent (anti-)BRST charges. The observation of the anticommutativity property of the (anti-)BRST charges is a novel result in view of the fact that we have taken into account only the (anti-)chiral super expansions. 1. Introduction The basic concepts behind the local gauge theories are at the heart of a precise theoretical description of three out of four fundamental interactions of nature. Becchi-Rouet-Stora- Tyutin (BRST) formalism [1–4] is one of the most intuitive and beautiful approaches to quantize the local gauge theories where the unitarity and quantum gauge (i.e., (anti-)BRST) invariance are respected together at any arbitrary order of perturbative computations for a given physical process that is permitted by the local (i.e., interacting) gauge theory at the quantum level. A couple of decisive features of the BRST formalism are the nilpotency of the (anti-)BRST symmetries as well as the existence of the absolute anticommutativity property between the BRST and anti-BRST symmetry trans- formations for a given local classical gauge transformation. The hallmark of the quantum (anti-)BRST symmetries is the existence of the (anti-)BRST invariant Curci-Ferrari- (CF-) type restriction(s) [5, 6] that ensure the absolute antic- ommutativity property of the (anti-)BRST symmetry transfor- mations and the existence of the coupled (but equivalent) Lagrangian densities for the quantum gauge theories. The Abelian 1-form gauge theory is an exception where the CF- type restriction is trivial and the Lagrangian density is unique (but that is a limiting case of the non-Abelian 1-form gauge theory where the CF condition [7] exists). The usual superfield approach (USFA) to BRST formal- ism [8–15] sheds light on the geometrical origin for the off- shell nilpotency and absolute anticommutativity of the (anti-)BRST symmetry transformations where the horizon- tality condition (HC) plays an important and decisive role [10–12]. These approaches, however, lead to the derivation of the (anti-)BRST symmetries for the gauge field and associ- ated (anti-)ghost fields only [10–12]. The above USFA does not shed any light on the (anti-)BRST symmetries, associated with the matter fields, in an interacting gauge theory. In our Hindawi Advances in High Energy Physics Volume 2020, Article ID 1236518, 25 pages https://doi.org/10.1155/2020/1236518