Abstract
We derive the off-shell nilpotent of order two and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST), anti-BRST, and (anti-)co-BRST symmetry transformations for the Christ–Lee (CL) model in one0+1-dimension (1D) of spacetime by exploiting the (anti-)chiral supervariable approach (ACSA) to BRST formalism where the quantum symmetry (i.e., (anti-)BRST along with (anti-)co-BRST) invariant quantities play a crucial role. We prove the nilpotency and absolute anticommutativity properties of the (anti-)BRST along with (anti-)co-BRST conserved charges within the scope of ACSA to BRST formalism where we take only one Grassmannian variable into account. We also show the (anti-)BRST and (anti-)co-BRST invariances of the Lagrangian within the scope of ACSA.
Highlights
Gauge theories describe three out of four fundamental interactions of nature which are characterized by first-class constraints in the context of Dirac’s prescription for the classification scheme of constraints [1, 2]
These symmetries are generated by the first-class constraints in a given gauge theory
We show the absolute anticommutativity as well as nilpotency properties ofBRST andco-BRST conserved charges within the realm of ACSA to BRST formalism
Summary
Gauge theories describe three (i.e., strong, weak, and electromagnetic) out of four fundamental interactions of nature which are characterized by first-class constraints in the context of Dirac’s prescription for the classification scheme of constraints [1, 2]. In this formalism, we have two fermionic-type global BRST ðsbÞ and anti-BRST ðsabÞ transformations at the quantum level (for a given local gauge symmetry transformation at the classical level) These symmetry transformations are endowed with two important properties: (i) nilpotency of order two (i.e., s2b = 0, s2ab = 0) and (ii) absolute anticommutativity (i.e., sb sab + sab sb = 0).
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