Abstract
We carry out the Becchi-Rouet-Stora-Tyutin (BRST) quantization of the one 0 + 1 -dimensional (1D) model of a free massive spinning relativistic particle (i.e., a supersymmetric system) by exploiting its classical infinitesimal and continuous reparameterization symmetry transformations. We use the modified Bonora-Tonin (BT) supervariable approach (MBTSA) to BRST formalism to obtain the nilpotent (anti-)BRST symmetry transformations of the target space variables and the (anti-)BRST invariant Curci-Ferrari- (CF-) type restriction for the 1D model of our supersymmetric (SUSY) system. The nilpotent (anti-)BRST symmetry transformations for other variables of our model are derived by using the (anti-)chiral supervariable approach (ACSA) to BRST formalism. Within the framework of the latter, we have shown the existence of the CF-type restriction by proving the (i) symmetry invariance of the coupled Lagrangians and (ii) the absolute anticommutativity property of the conserved (anti-)BRST charges. The application of the MBTSA to a physical SUSY system (i.e., a 1D model of a massive spinning particle) is a novel result in our present endeavor. In the application of ACSA, we have considered only the (anti-)chiral super expansions of the supervariables. Hence, the observation of the absolute anticommutativity of the (anti-)BRST charges is a novel result. The CF-type restriction is universal in nature as it turns out to be the same for the SUSY and non-SUSY reparameterization (i.e., 1D diffeomorphism) invariant models of the (non-)relativistic particles.
Highlights
The Becchi-Rouet-Stora-Tyutin (BRST) quantization scheme is one of the most elegant approaches to quantize the locally gauge and diffeomorphism invariant theories where the local classical transformation parameters are traded with theghost fields at the quantum level [1,2,3,4]
It is the usual superfield approach (USFA) to BRST formalism [8,9,10,11,12,13,14,15] which provides the interpretation and origin for the abstract mathematical properties that are associated with theBRST symmetries
We have not touched the continuous and infinitesimal reparameterization transformations (2). We focus on the latter classical symmetry transformations for the BRST analysis as it is our modest first step towards our main goal to discuss the diffeomorphism invariant SUSY theories in the physical ð3 + 1Þ
Summary
The Becchi-Rouet-Stora-Tyutin (BRST) quantization scheme is one of the most elegant approaches to quantize the locally gauge and diffeomorphism invariant theories where the local classical transformation parameters are traded with the (anti-)ghost fields at the quantum level [1,2,3,4]. We have derived the exact expression for the CF-type restriction by demanding (i) the invariance of the coupled (but equivalent) Lagrangians and (ii) the validity of the absolute anticommutativity of the off-shell nilpotent (anti-)BRST symmetries as well as conserved (anti-)BRST charges in the ordinary space and in the superspace (within the framework of ACSA to BRST formalism). These derivations of the CF-type restrictions, by various theoretical methods, are novel results in our present investigation. -dimensional (anti-)chiral super submanifolds of our chosen general ð1, 2Þ-dimensional supermanifold in the context of ACSA
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