Christ–Lee Model: (Anti-)chiral Supervariable Approach to BRST Formalism

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 one 0 + 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.

3D Jackiw-Pi Model: (Anti-)Chiral Superfield Approach to BRST Formalism

“…The BRST analysis of the non-Abelian JP model has been performed within the framework of AVSA to BRST formalism [23,24]. Against the backdrop of the above discussions, we have applied the newly proposed (anti-)chiral superfield formalism (ACSA) [33][34][35][36][37] to derive the complete set of (anti-)BRST symmetries as well as CF-condition of the theory where (anti-)chiral super expansions of the superfields (i.e. only one Grassmannian variable in expansions) have been taken into account.…”

Quantum symmetries and conserved charges of the cosmological Friedmann-Robertson-Walker model

“…The augmented version of the supervariable/superfield (AVSA) technique is the name given to this extended version of USFA. In light of the preceding discussions, we used the newly proposed (anti-)chiral supervariable/superfield formalism (ACSA) to derive the entire set of nilpotent (anti-)BRST symmetries where (anti-)chiral super expansions of the supervariables/superfields (with only one Grassmannian coordinate in the super expansions of the supervariables) have been taken into account (see, e.g., [37][38][39][40][41][42] for details). In our present endeavor, for the first time, the analysis of the BRST invariant cosmological model (i.e., FRW model) is discussed in the extended phase space within the realm of ACSA.…”