Nilpotent Symmetries and Conserved Charges: BRST-Quantized Version of the 4D Abelian 2-Form Gauge Theory
Abstract
We focus on the Becchi-Rouet-Stora-Tyutin (BRST) quantized version of the four (3 + 1)-dimensional (4D) free Abelian 2-form gauge theory and (i) discuss its infinitesimal, continuous and off-shell nilpotent (anti-)BRST and (anti-)co-BRST symmetry transformations, and (ii) derive the corresponding Noether conserved (anti-)BRST and (anti-)co-BRST charges. We demonstrate that these charges are not invariant under the above nilpotent symmetry transformations. We systematically derive the modified versions of the above Noether charges which are found to be invariant under the above symmetry transformations. As a consequence, both types of the above charges anticommute with each-other which proves their linear independence. We also derive the (anti-)BRST and (anti-)co-BRST invariant Curci-Ferrari (CF) type restrictions from the algebraic structures of the Noether conserved charges. In all the above proofs and derivations, we take into account the deep mathematical relationship that exists between the infinitesimal and continuous symmetry transformations and their generators as the Noether conserved charges.
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BibTeX
@misc{malik2026nilpotent,
title = {{Nilpotent Symmetries and Conserved Charges: BRST-Quantized Version of the 4D Abelian 2-Form Gauge Theory}},
author = {R. P. Malik},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.40025},
eprint = {2609.40025},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.40025},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Nilpotent Symmetries and Conserved Charges: BRST-Quantized Version of the 4D Abelian 2-Form Gauge Theory
AU - R. P. Malik
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2609.40025
UR - https://arxiv.org/abs/2609.40025
AB - We focus on the Becchi-Rouet-Stora-Tyutin (BRST) quantized version of the four (3 + 1)-dimensional (4D) free Abelian 2-form gauge theory and (i) discuss its infinitesimal, continuous and off-shell nilpotent (anti-)BRST and (anti-)co-BRST symmetry transformations, and (ii) derive the corresponding Noether conserved (anti-)BRST and (anti-)co-BRST charges. We demonstrate that these charges are not invariant under the above nilpotent symmetry transformations. We systematically derive the modified versions of the above Noether charges which are found to be invariant under the above symmetry transformations. As a consequence, both types of the above charges anticommute with each-other which proves their linear independence. We also derive the (anti-)BRST and (anti-)co-BRST invariant Curci-Ferrari (CF) type restrictions from the algebraic structures of the Noether conserved charges. In all the above proofs and derivations, we take into account the deep mathematical relationship that exists between the infinitesimal and continuous symmetry transformations and their generators as the Noether conserved charges.
ER -