Modified 3D Massive Abelian 2-Form Theory With a Single Pseudoscalar Field as a Phantom Field: BRST Approach

Abstract

We obtain the off-shell nilpotent Becchi–Rouet–Stora–Tyutin (BRST) and anti-BRST symmetry transformations (corresponding to the infinitesimal classical gauge symmetry transformations) for the modified massive three (2 + 1)-dimensional (3D) Abelian two-form gauge theory with a single pseudoscalar field. The latter field (having the negative kinetic term and a well-defined rest mass) has already been shown (i) to exist in the modified version of the standard 3D Stückelberg formalism (on the solid mathematical grounds), (ii) to be a possible candidate for the “phantom” field of some of the cosmological models of the universe, and (iii) to be a possible candidate for dark matter. These three results have been indicated in our earlier work. A couple of novel observations in our present endeavor are (i) the observation that, even though the pseudoscalar field does not transform under the gauge and (anti-)BRST symmetry transformations, it appears in the first-class constraints which annihilate the physical states at the quantum level, and (ii) the Noether conserved (anti-)BRST charges are found to be non-nilpotent. In our present investigation, the key results are the derivations of (i) the coupled (but equivalent) BRST and anti-BRST invariant Lagrangian densities, (ii) the conserved and off-shell nilpotent versions of the (anti-)BRST charges and the conserved ghost charge, (iii) the (anti-)BRST invariant Curci–Ferrari (CF) type restrictions, (iv) the standard BRST algebra amongst the conserved and nilpotent (anti-)BRST charges and conserved ghost charge, and (v) the explicit BRST-quantization of our 3D field-theoretic system. © © 2025 S. K. Panja et al. Advances in High Energy Physics published by John Wiley & Sons Ltd.