Noether Theorem and Nilpotency Property of the (Anti-)BRST Charges in the BRST Formalism: A Brief Review

Autor: Amit Kumar Rao, Ankur Tripathi, Bhupendra Chauhan, Rudra Prakash Malik
Jazyk: angličtina
Rok vydání: 2022
Předmět:
Zdroj: Universe, Vol 8, Iss 11, p 566 (2022)
Druh dokumentu: article
ISSN: 2218-1997
DOI: 10.3390/universe8110566
Popis: In some of the physically interesting gauge systems, we show that the application of the Noether theorem does not lead to the deduction of the Becchi–Rouet–Stora–Tyutin (BRST) and anti-BRST charges that obey precisely the off-shell nilpotency property despite the fact that these charges are (i) derived by using the off-shell nilpotent (anti-)BRST symmetry transformations, (ii) found to be the generators of the above continuous symmetry transformations, and (iii) conserved with respect to the time-evolution due to the Euler–Lagrange equations of motion derived from the Lagrangians/Lagrangian densities (that describe the dynamics of these suitably chosen physical systems). We propose a systematic method for the derivation of the off-shell nilpotent (anti-)BRST charges from the corresponding non-nilpotent Noether (anti-)BRST charges. To corroborate the sanctity and preciseness of our proposal, we take into account the examples of (i) the one (0 + 1)-dimensional (1D) system of a massive spinning (i.e., SUSY) relativistic particle, (ii) the D-dimensional non-Abelian one-form gauge theory, and (iii) the Abelian two-form and the Stu¨ckelberg-modified version of the massive Abelian three-form gauge theories in any arbitrary D-dimension of spacetime. Our present endeavor is a brief review where some decisive proposals have been made and a few novel results have been obtained as far as the nilpotency property is concerned.
Databáze: Directory of Open Access Journals
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