A field-theoretic model for Hodge theory

Gupta, Saurabh; Malik, R. P.

doi:10.1140/epjc/s10052-008-0758-4

Cited by 58 publications

(157 citation statements)

References 43 publications

Supporting

Mentioning

153

Contrasting

Order By: Relevance

“…However, these transformations have been found to be anticommuting only up to a U(1) vector gauge transformation. In our very recent works [43,44], we have derived the absolutely anticommuting set of (anti-)BRST as well as (anti-)co-BRST symmetry transformations and shown that the Abelian 2-form gauge theory is a field theoretic model for the Hodge theory. It would be very interesting to extend our present work and exploit the superfield approach to derive the above absolutely anticommuting (anti-)co-BRST symmetry transformations for the theory.…”

Section: Discussionmentioning

confidence: 99%

Abelian 2-form gauge theory: superfield formalism

Malik

2009

Eur. Phys. J. C

Self Cite

112

View full text Add to dashboard Cite

Abstract:We derive the off-shell nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for all the fields of a free Abelian 2-form gauge theory by exploiting the geometrical superfield approach to BRST formalism. The above four (3 + 1)-dimensional (4D) theory is considered on a (4, 2)-dimensional supermanifold parameterized by the four even spacetime variables x µ (with µ = 0, 1, 2, 3) and a pair of odd Grassmannian variables θ andθ (with θ 2 =θ 2 = 0, θθ +θθ = 0). One of the salient features of our present investigation is that the above nilpotent (anti-)BRST symmetry transformations turn out to be absolutely anticommuting due to the presence of a Curci-Ferrari (CF) type of restriction. The latter condition emerges due to the application of our present superfield formalism. The actual CF condition, as is well-known, is the hallmark of a 4D non-Abelian 1-form gauge theory. We demonstrate that our present 4D Abelian 2-form gauge theory imbibes some of the key signatures of the 4D non-Abelian 1-form gauge theory. We briefly comment on the generalization of our supperfield approach to the case of Abelian 3-form gauge theory in four (3 + 1)-dimensions of spacetime.

show abstract

Section: Discussionmentioning

confidence: 99%

Abelian 2-form gauge theory: superfield formalism

Malik

2009

Eur. Phys. J. C

Self Cite

112

View full text Add to dashboard Cite

show abstract

“…As pointed out after (19) and (25), the brackets {b † , b † } = 0 and {b, b} = 0 are not produced by the pairs (s 1 , Q) and (s 2 ,Q), respectively. However, the transformations s ω (generated by Q ω ) produce all the appropriate (anti)commutators as is illustrated in (30).…”

Section: Discussionmentioning

confidence: 68%

“…We have proven that the 1D model of a rigid rotor [17], N = 2 SUSY quantum mechanical model with any arbitrary superpotential [16], N = 2 SUSY model for the motion of a charged particle under influence of a magnetic field [18], free 4D Abelian 2-form and 6D Abelian 3-form gauge theories [19][20][21], etc., are models for the Hodge theory. For all these models, we can perform the canonical quantization without taking recourse to the mathematical definition of the canonical conjugate momenta.…”

Section: Discussionmentioning

confidence: 99%

𝒩 = 2 supersymmetric harmonic oscillator: Basic brackets without canonical conjugate momenta

Srinivas

Shukla

Malik

2015

Int. J. Mod. Phys. A

Self Cite

View full text Add to dashboard Cite

Abstract:We exploit the ideas of spin-statistics theorem, normal-ordering and the key concepts behind the symmetry principles to derive the canonical (anti)commutators for the case of a one (0 + 1)-dimensional (1D) N = 2 supersymmetric (SUSY) harmonic oscillator (HO) without taking the help of the mathematical definition of canonical conjugate momenta with respect to the bosonic and fermionic variables of this toy model for the Hodge theory (where the continuous and discrete symmetries of the theory provide the physical realizations of the de Rham cohomological operators of differential geometry). In our present endeavor, it is the full set of continuous symmetries and their corresponding generators that lead to the derivation of basic (anti)commutators amongst the creation and annihilation operators that appear in the normal mode expansions of the dynamical fermionic and bosonic variables of our present N = 2 SUSY theory of a HO. These basic brackets are in complete agreement with such kind of brackets that are derived from the standard canonical method of quantization scheme.

show abstract

“…It has been shown, within the framework of BRST formalism, that the 4D free Abelian 2-form gauge theory provides a tractable field-theoretic model for Hodge theory where de Rham cohomological operators of differential geometry and Hodge duality operation find their physical realizations in terms of the continuous and discrete symmetries, respectively [36]. Furthermore, it has also shown to be a quasi-topological field theory (q-TFT) which captures some features of Witten-type TFT and some aspects of Schwartztype TFT [37].…”

Section: Introductionmentioning

confidence: 99%

$$(3+1)$$ ( 3 + 1 ) -Dimensional topologically massive 2-form gauge theory: geometrical superfield approach

Kumar¹,

Mukhopadhyay²

2018

Eur. Phys. J. C

View full text Add to dashboard Cite

We derive the complete set of off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations corresponding to the combined "scalar" and "vector" gauge symmetry transformations for the (3+1)-dimensional (4D) topologically massive non-Abelian (B ∧ F) theory with the help of geometrical superfield formalism. For this purpose, we use three horizontality conditions (HCs). The first HC produces the (anti-)BRST transformations for the 1-form gauge field and corresponding (anti-)ghost fields whereas the second HC yields the (anti-)BRST transformations for 2-form field and associated (anti-)ghost fields. The integrability of second HC produces third HC. The latter HC produces the (anti-)BRST symmetry transformations for the compensating auxiliary vector field and corresponding ghosts. We obtain five (anti-)BRST invariant Curci-Ferrari (CF)-type conditions which emerge very naturally as the off-shoots of superfield formalism. Out of five CF-type conditions, two are fermionic in nature. These CF-type conditions play a decisive role in providing the absolute anticommutativity of the (anti-)BRST transformations and also responsible for the derivation of coupled but equivalent (anti-)BRST invariant Lagrangian densities. Furthermore, we capture the (anti-)BRST invariance of the coupled Lagrangian densities in terms of the superfields and translation generators along the Grassmannian directions θ andθ .

show abstract

A field-theoretic model for Hodge theory

Cited by 58 publications

References 43 publications

Abelian 2-form gauge theory: superfield formalism

Abelian 2-form gauge theory: superfield formalism

𝒩 = 2 supersymmetric harmonic oscillator: Basic brackets without canonical conjugate momenta

$$(3+1)$$ ( 3 + 1 ) -Dimensional topologically massive 2-form gauge theory: geometrical superfield approach

Contact Info

Product

Resources

About