Superfield approach to symmetry invariance in quantum electrodynamics with complex scalar fields

Malik, R. P.; Mandal, Bhabani Prasad

doi:10.1007/s12043-009-0073-0

Cited by 3 publications

(8 citation statements)

References 42 publications

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“…the Grassmannian variables, on the appropriate (4, 2)-dimensional super Lagrangian density, turns out to be zero, the corresponding 4D Lagrangian density of a given gauge theory would respect the nilpotent (anti-)BRST symmetry invariance. This conclusion is in complete agreement with our recent works on 1-form gauge theories [36][37][38][39]. We wrap up this section with the assertion that the superfield approach to BRST formalism does simplify the understanding of the (anti-)BRST invariance in a given theory.…”

Section: (Anti-)brst Invariance: Superfield Approachsupporting

confidence: 88%

Abelian 2-form gauge theory: superfield formalism

Malik

2009

Eur. Phys. J. C

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112

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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.

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Section: (Anti-)brst Invariance: Superfield Approachsupporting

confidence: 88%

Abelian 2-form gauge theory: superfield formalism

Malik

2009

Eur. Phys. J. C

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112

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“…The generic field Ω(x) stands for the 4D matter Dirac fields ψ(x) andψ(x). There is an interesting consequence due to our expansion in (19). It is straightforward to check that the following equation…”

Section: (Anti-)brst Symmetry Transformations For Dirac Fields: Gaugementioning

confidence: 90%

“…L (d) ) remains unaffected due to the presence of the Grassmannian variables on the (4, 2)-dimensional supermanifold, on which, our 4D interacting U(1) gauge theory (with Dirac fields) has been generalized. The above observation implies that the super Lagrangian density for the Dirac fields, using GIR (16) and super expansion (19), can be written…”

Section: (Anti-)brst Symmetry Transformations For Dirac Fields: Gaugementioning

confidence: 95%

“…(16)) on the matter superfields leads to (i) the exact and unique derivation of the nilpotent (anti-)BRST symmetry transformations for the matter fields ψ(x) andψ(x), and (ii) the geometrical interpretation for the (anti-)BRST symmetry transformations as the translational generators along the Grassmannian directions θ andθ of the above supermanifold. As a consequence, we obtain the analogue of the equation (10), as (20) whereΩ (G) (x, θ,θ) stands for the expansions (19) for the matter superfields, obtained after the application of the GIR (16). The generic field Ω(x) stands for the 4D matter Dirac fields ψ(x) andψ(x).…”

Section: (Anti-)brst Symmetry Transformations For Dirac Fields: Gaugementioning

confidence: 99%

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Symmetry Invariance, Anticommutativity and Nilpotency in BRST Approach to QED: Superfield Formalism

Malik

2011

J. Phys. Math.

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We provide the geometrical interpretation for the Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry invariance of the Lagrangian density of a four (3 + 1)-dimensional (4D) interacting U(1) gauge theory within the framework of superfield approach to BRST formalism. This interacting theory, where there is an explicit coupling between the U(1) gauge field and matter (Dirac) fields, is considered on a (4, 2)-dimensional supermanifold parametrized by the four spacetime variables x µ (µ = 0, 1, 2, 3) and a pair of Grassmannian variables θ andθ (with θ 2 =θ 2 = 0, θθ +θθ = 0). We express the Lagrangian density and (anti-)BRST charges in the language of the superfields and show that (i) the (anti-)BRST invariance of the 4D Lagrangian density is equivalent to the translation of the super Lagrangian density along the Grassmannian direction(s) (θ and/orθ) of the (4, 2)-dimensional supermanifold such that the outcome of the above translation(s) is zero, and (ii) the anticommutativity and nilpotency of the (anti-)BRST charges are the automatic consequences of our superfield formulation. PACS numbers: 11.15.-q, 12.20.-m, 03.70.+k Keywords: QED with Dirac fields, nilpotent (anti-)BRST symmetry invariance, superfield formalism, horizontality condition, gauge invariant condition on the matter superfields, geometrical interpretation(s)The usual superfield approach [1-8] to BRST formalism has been very successfully applied to the case of 4D (non-)Abelian 1-form (A (1) = dx µ A µ ) gauge theories. In this approach, one constructs a super curvature 2-form F (2) =dÃ (1) + iÃ (1) ∧Ã (1) by exploiting the Maurer-Cartan equation in the language of the super 1-form gauge connectionÃ (1) and the super exterior derivatived = dZ M ∂ M ≡ dx µ ∂ µ + dθ∂ θ + dθ∂θ (withd 2 = 0) that are defined on a (4, 2)-dimensional supermanifold, parametrized by the superspace variables Z M = (x µ , θ,θ) (with the super derivatives ∂ M = (∂ µ , ∂ θ , ∂θ)).The above super curvature is subsequently equated to the ordinary 2form curvature F (2) = dA (1) + iA (1) ∧ A (1) (with d = dx µ ∂ µ and A (1) = dx µ A µ ) defined on the 4D ordinary flat Minkowskian spacetime manifold that is parametrized by the ordinary spacetime variable x µ (µ = 0, 1, 2, 3). This restriction, popularly known as the horizontality condition, leads to the derivation of the nilpotent (anti-)BRST symmetry transformations for the gauge and (anti-)ghost fields of the 4D (non-)Abelian 1-form gauge theories.The key reasons behind the emergence of the nilpotent (anti-)BRST symmetry transformations for the gauge and (anti-)ghost fields, due to the above horizontality condition 1 (HC), are (i) the nilpotency of the (super) exterior derivatives (d)d which play very important roles in the above HC, and (ii) the super 1-form connectionÃ (1) = dZ MÃ M involves the vector super-fieldÃ M that consists of the multiplet superfields (B µ , F ,F) which are nothing but the generalizations of the gauge and (anti-)ghost fields (A µ , C,C). The latter are the basic fields of the 4D (non-)Abelian 1-form gaug...

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“…the Refs. [186][187][188][189][190][191][192][193], gives a particle mass. Scalar quantum electrodynamics, Cf.…”

Section: Introductionmentioning

confidence: 99%

Challenging Photon Mass: from Scalar Quantum Electrodynamics to String Theory

Glinka¹

2014

AMP

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A massless photon, originated already through the Maxwell theory of electromagnetism, is one of the basic paradigms of modern physics, ideally supported throughout both the quantum electrodynamics and the Higgs mechanism of spontaneous symmetry breaking which lays the foundations of the Standard Model of elementary particles and fundamental interactions. Nevertheless, the physical interpretation of the optical experimental data, such like observations of total internal reflection of the beam shift in the Goos-H¨anchen effect, concludes a photon mass. Is, therefore, light diversified onto two independent species -gauge photons and optical photons? Can such a state of affairs be consistently described through a unique theoretical model? In this paper, two models of a photon mass, arising from the scalar quantum electrodynamics with the Higgs potential, are discussed. The first scenario leads to a neutral scalar mass estimable throughout the experimental limits on a photon mass. In the modified mechanism, a neutral scalar mass in not affected throughout a photon mass and is determinable through the experimental data, while a massless dilaton is present and a non-kinetic massive vector field effectively results in the string theory of non-interacting invariant both a free photon and a neutral scalar, and the Aharonov-Bohm effect is considered. The Markov hypothesis on maximality of the Planck mass is applied.

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Superfield approach to symmetry invariance in quantum electrodynamics with complex scalar fields

Cited by 3 publications

References 42 publications

Abelian 2-form gauge theory: superfield formalism

Abelian 2-form gauge theory: superfield formalism

Symmetry Invariance, Anticommutativity and Nilpotency in BRST Approach to QED: Superfield Formalism

Challenging Photon Mass: from Scalar Quantum Electrodynamics to String Theory

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