Abstract
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 0+1-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.
Highlights
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
The hallmark of the quantum gauge theory is encoded in the existence of the CF-type restriction which we have demonstrated in Equations (14), (19), (22), and (23) where we have concentrated on the quantumBRST symmetries which are respected by the coupled Lagrangians Lb and Lb
We have exploited the basic idea of ACSA to BRST formalism where we have demanded that the anti-BRST invariant quantities must be independent of the Grassmannian variable θ when they are generalized onto the ð1, 1Þ-dimensional chiral super submanifold of the general (1, 2)-dimensional supermanifold
Summary
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. (CF-) type restriction(s) [5, 6] that ensure the absolute anticommutativity property of the (anti-)BRST symmetry transformations and the existence of the coupled (but equivalent) Lagrangian densities for the quantum gauge theories. Against the backdrop of the above discussions, in our present endeavor, we have shown the existence of the three classical level symmetries which are the gauge, supergauge, and reparameterization transformations (cf Equations (2) and (4)) under which the first-order Lagrangian ðLf Þ for the 1D system of a massive spinning relativistic particle remains invariant. We have captured all the above key features within the framework of ACSA to BRST formalism where only the (anti-)chiral supervariables and their corresponding super expansion(s) along the Grassmannian direction(s) of the (1, 1)-dimensional (anti-)chiral super submanifolds of the general (1, 2)-dimensional supermanifold have been taken into consideration in a consistent and systematic fashion. We denote the (anti-)BRST charges by the symbol QðaÞb
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