2025

Permanent URI for this collectionhttps://dl.bhu.ac.in/bhuir/handle/123456789/62057

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Modified 3D Massive Abelian 2-Form Theory With a Single Pseudoscalar Field as a Phantom Field: BRST Approach
(John Wiley and Sons Ltd, 2025) Suman Kumar Panja; E. Harikumar; Rudra Prakash Malik
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.
Pseudoscalar Field as a Possible Candidate for Phantom Field
(John Wiley and Sons Ltd, 2025) E. Harikumar; Rudra Prakash Malik
We demonstrate the existence of a single pseudoscalar (PS) field in the mathematically backed and parity-preserving modifications of the standard Stückelberg formalism (SSF) in the context of the Lagrangian formulation of the (i) two (1 + 1)-dimensional (2D) massive Abelian 1-form gauge theory, (ii) three (2 + 1)-dimensional (3D) massive Abelian 2-form gauge theory, and (iii) four (3 + 1)-dimensional (4D) massive Abelian 3-form gauge theory. This PS field always turns up with the (i) negative kinetic term and (ii) higher order derivative terms. The latter terms are rendered into the well-defined terms due to the imposition of the on-shell condition for the PS field which is derived from the properly gauge-fixed Lagrangian densities for the above theories. These Lagrangian densities incorporate into themselves the (i) PS field with the negative kinetic term and (ii) pure scalar field with the positive kinetic term. However, both these fields satisfy the Klein–Gordon (KG) equation of motion. The PS field (having the negative kinetic term and a well-defined mass) is one of the possible candidates for the “phantom” field which plays a crucial role in the cyclic, bouncing, and self-accelerated cosmological models of the universe. The “exotic” PS field also satisfies one of the criteria for being a possible candidate for dark matter. © © 2025 E. Harikumar and R. P. Malik. Advances in High Energy Physics published by John Wiley & Sons Ltd.