Modified 3D Massive Abelian 2-From Theory with a Single Pseudo-Scalar Field as a Phantom Field: BRST Approach
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arXiv
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| Format: | Preprint |
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2024
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| author | Panja, S. K. Harikumar, E. Malik, R. P. |
| author_facet | Panja, S. K. Harikumar, E. Malik, R. P. |
| contents | 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 2-form gauge theory with a single pseudo-scalar field. The latter field (having the negative kinetic term and a well-defined mass) has already been shown (i) to exist in the modified version of the standard 3D St${\ddot u}$ckelberg 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. A couple of highlights of our present endeavor are (i) the observation that, even though the pseudo-scalar 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, we derive (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, and (iv) the standard BRST algebra amongst the conserved and nilpotent (anti-)BRST charges and conserved ghost charge of our theory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_15588 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Modified 3D Massive Abelian 2-From Theory with a Single Pseudo-Scalar Field as a Phantom Field: BRST Approach Panja, S. K. Harikumar, E. Malik, R. P. High Energy Physics - Theory 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 2-form gauge theory with a single pseudo-scalar field. The latter field (having the negative kinetic term and a well-defined mass) has already been shown (i) to exist in the modified version of the standard 3D St${\ddot u}$ckelberg 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. A couple of highlights of our present endeavor are (i) the observation that, even though the pseudo-scalar 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, we derive (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, and (iv) the standard BRST algebra amongst the conserved and nilpotent (anti-)BRST charges and conserved ghost charge of our theory. |
| title | Modified 3D Massive Abelian 2-From Theory with a Single Pseudo-Scalar Field as a Phantom Field: BRST Approach |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2405.15588 |