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arXiv · 2603.24514

Canonical Brackets, (Anti-)BRST Invariant Charges and Physicality Criteria: Non-Abelian 1-Form Gauge Theory

R. P. Malik
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Abstract

In the case of a D-dimensional non-Abelian 1-form gauge theory (without any interaction with the matter fields), we show that the application of the Noether theorem does not lead to the derivations of the Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST charges that obey (i) the (anti-)BRST invariance, and (ii) the nilpotency property (unless we exploit the theoretical strength of $(a)$ the partial integration along with the Gauss divergence theorem, and $(b)$ use the appropriate equations of motion at suitable places). This happens because of the presence of a non-trivial Curci-Ferrari (CF) condition on our BRST-quantized D-dimensional non-Abelian 1-form gauge theory (whose limiting case is the BRST-quantized D-dimensional Abelian 1-form gauge theory where the CF-type restriction is trivial and the corresponding Noether (anti-)BRST charges turn out to be nilpotent as well as (anti-)BRST invariant quantities together). We exploit the theoretical strength of the basic canonical (anti)commutators to prove (i) the Noether (anti-)BRST charges as the true generators for the off-shell nilpotent (anti-)BRST symmetry transformations, and (ii) the (anti-)BRST invariance of the consistently modified versions of the Noether (anti-)BRST charges. We demonstrate that the (anti-)BRST invariant versions of the conserved (anti-)BRST charges are useful in the discussion on the physicality criteria because of their consistency with the Dirac quantization conditions for the gauge theories.

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R. P. Malik. 2026-03-25. Canonical Brackets, (Anti-)BRST Invariant Charges and Physicality Criteria: Non-Abelian 1-Form Gauge Theory. https://arxiv.org/abs/2603.24514

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