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

Abstract

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.

Canonical brackets of a toy model for the Hodge theory without its canonical conjugate momenta

“…For instance, such theories are Abelian p-form (p = 1, 2, 3) gauge theories which have been shown to be the field theoretic models for the Hodge theory in D = 2p dimensions of spacetime (see, e.g. [12][13][14][15][16]). These theories respect six continuous symmetries that lead to the derivation of canonical basic brackets amongst the creation and annihilation operators.…”

“…We have proposed many models for the Hodge theory which are from the domains of p-form (p = 1, 2, 3) gauge theories [12][13][14][15][16] and N = 2 SUSY quantum mechanics [17][18][19]. One of the decisive features of the models for the Hodge theories, connected with the p-form gauge theories, is that these theories are always endowed with six continuous symmetries within the framework of BRST formalism.…”

Superspace Unitary Operator in Superfield Approach to Non-Abelian Gauge Theory with Dirac Fields

“…The discussion about the nilpotent (anti-)co-BRST symmetry transformations and the corresponding dual SUSP unitary operators has been achieved in our very recent work [22]. In this context, it is very gratifying to state that we have also derived the dual SUSP unitary operator and its Hermitian conjugate which lead to the derivation of the proper (anti-)co-BRST symmetry transformations for some of the interesting Abelian models [18][19][20] Thus, as far as the symmetry properties are concerned, the Lagrangian densities L and L are equivalent on the hypersurface (in the 4D Minkowskian spacetime manifold) where the CF-condition + + × = 0 is satisfied. In fact, the absolute anticommutativity property ( + = 0) of the (anti-)BRST symmetry transformations ( ) is also true only on this hypersurface.…”

“…In our earlier works [18][19][20], we have derived the nilpotent (anti-)BRST and (anti-)co-BRST symmetry transformations for the Stueckelberg-modified version of the 2D Proca theory [18], the modified version of the 2D anomalous gauge theory [19], and the 2D self-dual chiral bosonic field theory [20] by exploiting the tools and techniques of the augmented version of geometrical superfield formalism [8][9][10]. We lay emphasis on the fact that, in these theories [18][19][20], we have the presence of the matter as well as gauge fields which are coupled to one another in a specific fashion. Thus, it would be very nice idea to find out the SUSP unitary operators for these theories where not only the off-shell nilpotent (anti-)BRST symmetry transformations but also the off-shell nilpotent (anti-)co-BRST symmetries exist, too, for the matter, gauge, and (anti)ghost fields.…”

A precisely feasible gauged model of chiral boson with its BRST cohomological perspectives

“…So along with the nilpotent BRST symmetry, we concentrate on the other nilpotent symmetries like ant-BRST, co-BRST, and anti-co-BRST symmetry in this framework systematically. There are a few investigations where endeavors have been made for various models to show that the generators of of the symmetries related to the BRST resembles the algebraic structure of de Rham cohomological operator of differential geometry [45,[49][50][51][52][53][54][55][56][57][58][59][60][61][62][63]. A unique endeavor in this manner is made here to analyze whether the generators of these continuous symmetries satisfy algebra of de Rham cohomological operators of differential geometry.…”