Gauge Transformations, BRST Cohomology and Wigner's Little Group

Malik, R. P.

doi:10.1142/s0217751x04018361

Cited by 13 publications

(28 citation statements)

References 37 publications

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“…The emergence of such kinds of fields is nothing new. This kind of kinetic term turned up, very naturally, in the context of 4D Abelian 2-form gauge theory [15][16][17][18] when the latter was proven to provide a model for the Hodge theory. Obviously, such kind of particles have not yet been detected by the experiments in high energy physics.…”

Section: Discussionmentioning

confidence: 99%

Novel symmetries in the modified version of two dimensional Proca theory

2013

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By exploiting the Stueckelberg approach, we obtain a gauge theory for the two (1+1)-dimensional (2D) Proca theory and demonstrate that this theory is endowed with, in addition to the usual Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetries, the on-shell nilpotent (anti-)co-BRST symmetries, under which, the total gauge-fixing term remains invariant. The anticommutator of the BRST and co-BRST (as well as anti-BRST and anti-co-BRST) symmetries define a unique bosonic symmetry in the theory, under which, the ghost part of the Lagrangian density remains invariant. To establish connections of the above symmetries with the Hodge theory, we invoke a pseudo-scalar field in the theory. Ultimately, we demonstrate that the full theory provides a field theoretic example for the Hodge theory where the continuous symmetry transformations provide a physical realization of the de Rham cohomological operators and discrete symmetries of the theory lead to the physical realization of the Hodge duality operation of differential geometry. We also mention the physical implications and utility of our present investigation.

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Section: Discussionmentioning

confidence: 99%

Novel symmetries in the modified version of two dimensional Proca theory

2013

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“…Its quasi-topological nature has been discussed in [39] and it has been shown that this theory provides a tractable field theoretical model for the Hodge theory in 4D [38,39]. The "extended" BRST cohomology for this theory has been discussed in [40] where the insights from the Wigner's little group play a very crucial role. It would be interesting endeavour to capture the (anti-)BRST and (anti-)co-BRST symmetries for the above 2-form Abelian gauge theory in the framework of superfield formalism and provide geometrical origin for the nilpotent charges in the theory.…”

Section: Discussionmentioning

confidence: 99%

Superfield approach to (non-)local symmetries for 1-form Abelian gauge theory

Malik¹

2004

J. Phys. A: Math. Gen.

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Abstract:We exploit the geometrical superfield formalism to derive the local, covariant and continuous Becchi-Rouet-Stora-Tyutin (BRST) symmetry transformations and the non-local, non-covariant and continuous dual-BRST symmetry transformations for the free Abelian one-form gauge theory in four (3+1)-dimensions (4D) of spacetime. Our discussion is carried out in the framework of BRST invariant Lagrangian density for the above 4D theory in the Feynman gauge. The geometrical origin and interpretation for the (dual-)BRST charges (and the transformations they generate) are provided in the language of translations of some superfields along the Grassmannian directions of the six (4 + 2)-dimensional supermanifold parametrized by the four spacetime and two Grassmannian variables. *

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“…It is to be remarked that the absolute anticommutativity of the (anti-) BRST symmetry transformations imply that only one of them would be really the analogue of the exterior derivative (see, equations (28), (69) below). In a similar fashion, it can be seen that the following off-shell nilpotent (s 2 a(d) = 0) and absolutely anticommuting (s d s ad +s ad s d = 0) (anti-) co-BRST symmetry transformations (s (a)d )…”

Section: Absolutely Anticommuting (Anti-) Brst and (Anti-) Co-brst Symentioning

confidence: 99%

On free 4D Abelian 2-form and anomalous 2D Abelian 1-form gauge theories

2009

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We demonstrate a few striking similarities and some glaring differences between (i) the free four (3 + 1)-dimensional (4D) Abelian 2-form gauge theory, and (ii) the anomalous two (1 + 1)-dimensional (2D) Abelian 1-form gauge theory, within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism. We demonstrate that the Lagrangian densities of the above two theories transform in a similar fashion under a set of symmetry transformations even though they are endowed with a drastically different variety of constraint structures. Taking the help of our understanding of the 4D Abelian 2-form gauge theory, we prove that the gauge invariant version of the anomalous 2D Abelian 1-form gauge theory is a new field-theoretic model for the Hodge theory where all the de Rham cohomological operators of differential geometry find their physical realizations in the language of proper symmetry transformations. The corresponding conserved charges obey an algebra that is reminiscent of the algebra of the cohomological operators. We briefly comment on the consistency of the 2D anomalous 1-form gauge theory in the language of restrictions on the harmonic state of the (anti-) BRST and (anti-) co-BRST invariant version of the above 2D theory.

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Gauge Transformations, BRST Cohomology and Wigner's Little Group

Cited by 13 publications

References 37 publications

Novel symmetries in the modified version of two dimensional Proca theory

Novel symmetries in the modified version of two dimensional Proca theory

Superfield approach to (non-)local symmetries for 1-form Abelian gauge theory

On free 4D Abelian 2-form and anomalous 2D Abelian 1-form gauge theories

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