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(Anti-)chiral supervariable approach to nilpotent and absolutely anticommuting conserved charges of reparametrization invariant theories: A couple of relativistic toy models as examples

S. KUMAR

http://orcid.org/0000-0003-1484-4258

Physics Department, Centre of Advanced Studies, Banaras Hindu University, Varanasi 221005, (U.P.), India

E-mail Address: sunil.bhu93@gmail.com

Corresponding author.

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B. Chauhan

Physics Department, Centre of Advanced Studies, Banaras Hindu University, Varanasi 221005, (U.P.), India

E-mail Address: bchauhan501@gmail.com

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, and

R. P. Malik

Physics Department, Centre of Advanced Studies, Banaras Hindu University, Varanasi 221005, (U.P.), India

DST Centre for Interdisciplinary Mathematical Sciences, Institute of Science, Banaras Hindu University, Varanasi 221005, India

E-mail Address: rpmalik1995@gmail.com

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https://doi.org/10.1142/S0217751X18501336Cited by:8 (Source: Crossref)

Abstract

We exploit the potential and power of the Becchi–Rouet–Stora–Tyutin (BRST) and anti-BRST invariant restrictions on the (anti-)chiral supervariables to derive the proper nilpotent (anti-)BRST symmetries for the reparametrization invariant one (0+1)-dimensional (1D) toy models of a free relativistic particle as well as a free spinning (i.e. supersymmetric) relativistic particle within the framework of (anti-)chiral supervariable approach to BRST formalism. Despite the (anti-)chiral super expansions of the (anti-)chiral supervariables, we observe that the (anti-)BRST charges, for the above toy models, turn out to be absolutely anticommuting in nature. This is one of the novel observations of our present endeavor. For this proof, we utilize the beauty and strength of Curci–Ferrari (CF)-type restriction in the context of a spinning relativistic particle but no such restriction is required in the case of a free scalar relativistic particle. We have also captured the nilpotency property of the conserved charges as well as the (anti-)BRST invariance of the appropriate Lagrangian(s) of our present toy models within the framework of (anti-)chiral supervariable approach.

Keywords:

PACS: 11.15.-q, 11.30.Pb

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