Superfield approach to symmetry invariance in QED with complex scalar fields

We show that the Grassmannian independence of the super Lagrangian density, expressed in terms of the superfields defined on a (4, 2)-dimensional supermanifold, is a clear-cut proof for the Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST invariance of the corresoponding four (3 + 1)-dimensional (4D) Lagrangian density that describes the interaction between the U(1) gauge field and the charged complex scalar fields. The above 4D field theoretical model is considered on a (4, 2)-dimensional supermanifold parametrized by the ordinary four spacetime variables x^\mu (with \mu = 0, 1, 2, 3) and a pair of Grassmannian variables \theta and \bar\theta (with \theta^2 = \bar\theta^2 = 0, \theta \bar\theta + \bar\theta \theta = 0). Geometrically, the (anti-)BRST invariance is encoded in the translation of the super Lagrangian density along the Grassmannian directions of the above supermanifold such that the outcome of this shift operation is zero.Comment: LaTeX file, 14 pages, minor changes in the title and text, version to appear in ``Pramana - Journal of Physics'

Gauge Transformations, BRST Cohomology and Wigner's Little Group

We discuss the (dual-)gauge transformations and BRST cohomology for the two (1 + 1)-dimensional (2D) free Abelian one-form and four (3 + 1)-dimensional (4D) free Abelian 2-form gauge theories by exploiting the (co-)BRST symmetries (and their corresponding generators) for the Lagrangian densities of these theories. For the 4D free 2-form gauge theory, we show that the changes on the antisymmetric polarization tensor e^{\mu\nu} (k) due to (i) the (dual-)gauge transformations corresponding to the internal symmetry group, and (ii) the translation subgroup T(2) of the Wigner's little group, are connected with each-other for the specific relationships among the parameters of these transformation groups. In the language of BRST cohomology defined w.r.t. the conserved and nilpotent (co-)BRST charges, the (dual-)gauge transformed states turn out to be the sum of the original state and the (co-)BRST exact states. We comment on (i) the quasi-topological nature of the 4D free 2-form gauge theory from the degrees of freedom count on e^{\mu\nu} (k), and (ii) the Wigner's little group and the BRST cohomology for the 2D one-form gauge theory {\it vis-{\`a}-vis} our analysis for the 4D 2-form gauge theory.Comment: LaTeX file, 29 pages, misprints in (3.7), (3.8), (3.9), (3.13) and (4.14)corrected and communicated to IJMPA as ``Erratum'

Geometrical Aspects Of BRST Cohomology In Augmented Superfield Formalism

In the framework of augmented superfield approach, we provide the geometrical origin and interpretation for the nilpotent (anti-)BRST charges, (anti-)co-BRST charges and a non-nilpotent bosonic charge. Together, these local and conserved charges turn out to be responsible for a clear and cogent definition of the Hodge decomposition theorem in the quantum Hilbert space of states. The above charges owe their origin to the de Rham cohomological operators of differential geometry which are found to be at the heart of some of the key concepts associated with the interacting gauge theories. For our present review, we choose the two $(1 + 1)$-dimensional (2D) quantum electrodynamics (QED) as a prototype field theoretical model to derive all the nilpotent symmetries for all the fields present in this interacting gauge theory in the framework of augmented superfield formulation and show that this theory is a {\it unique} example of an interacting gauge theory which provides a tractable field theoretical model for the Hodge theory.Comment: LaTeX file, 25 pages, Ref. [49] updated, correct page numbers of the Journal are give

Wigner's little group and BRST cohomology for one-form Abelian gauge theory

We discuss the (dual-)gauge transformations for the gauge-fixed Lagrangian density and establish their intimate connection with the translation subgroup T(2) of the Wigner's little group for the free one-form Abelian gauge theory in four $(3 + 1)$-dimensions (4D) of spacetime. Though the relationship between the usual gauge transformation for the Abelian massless gauge field and T(2) subgroup of the little group is quite well-known, such a connection between the dual-gauge transformation and the little group is a new observation. The above connections are further elaborated and demonstrated in the framework of Becchi-Rouet-Stora-Tyutin (BRST) cohomology defined in the quantum Hilbert space of states where the Hodge decomposition theorem (HDT) plays a very decisive role.Comment: LaTeX file, 17 pages, Journal-ref. give

Superfield Approach to (Non-)local Symmetries for One-Form Abelian Gauge Theory

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.Comment: LaTeX file, 23 page

Superfield Approach To Nilpotent Symmetries For QED From A Single Restriction: An Alternative To The Horizontality Condition

We derive together the exact local, covariant, continuous and off-shell nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the U(1) gauge field (A_\mu), the (anti-)ghost fields ((\bar C)C) and the Dirac fields (\psi, \bar\psi) of the Lagrangian density of a four (3 + 1)-dimensional QED by exploiting a single restriction on the six (4, 2)-dimensional supermanifold. A set of four even spacetime coordinates x^\mu (\mu = 0, 1, 2, 3) and two odd Grassmannian variables \theta and \bar\theta parametrize this six dimensional supermanifold. The new gauge invariant restriction on the above supermanifold owes its origin to the (super) covariant derivatives and their intimate relations with the (super) 2-form curvatures (\tilde F^{(2)})F^{(2)} constructed with the help of (super) 1-form gauge connections (\tilde A^{(1)})A^{(1)} and (super) exterior derivatives (\tilde d)d. The results obtained separately by exploiting (i) the horizontality condition, and (ii) one of its consistent extensions, are shown to be a simple consequence of this new single restriction on the above supermanifold. Thus, our present endeavour provides an alternative to (and, in some sense, generalization of) the horizontality condition of the usual superfield formalism applied to the derivation of BRST symmetries.Comment: LaTeX file, 15 pages, journal-versio

Nilpotent Symmetries For Matter Fields In Non-Abelian Gauge Theory: Augmented Superfield Formalism

In the framework of superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism, the derivation of the (anti-)BRST nilpotent symmetries for the matter fields, present in any arbitrary interacting gauge theory, has been a long-standing problem. In our present investigation, the local, covariant, continuous and off-shell nilpotent (anti-)BRST symmetry transformations for the Dirac fields $(\psi, \bar\psi)$ are derived in the framework of the augmented superfield formulation where the four $(3 + 1)$-dimensional (4D) interacting non-Abelian gauge theory is considered on the six $(4 + 2)$-dimensional supermanifold parametrized by the four even spacetime coordinates $x^\mu$ and a couple of odd elements ($\theta$ and $\bar\theta$) of the Grassmann algebra. The requirement of the invariance of the matter (super)currents and the horizontality condition on the (super)manifolds leads to the derivation of the nilpotent symmetries for the matter fields as well as the gauge- and the (anti-)ghost fields of the theory in the general scheme of the augmented superfield formalism.Comment: LaTeX file, 16 pages, printing mistakes in the second paragraph of `Introduction' corrected, a footnote added, these modifications submitted as ``erratum'' to IJMPA in the final for

Hodge Duality Operation And Its Physical Applications On Supermanifolds

An appropriate definition of the Hodge duality $\star$ operation on any arbitrary dimensional supermanifold has been a long-standing problem. We define a working rule for the Hodge duality $\star$ operation on the $(2 + 2)$-dimensional supermanifold parametrized by a couple of even (bosonic) spacetime variables $x^\mu (\mu = 0, 1)$ and a couple of Grassmannian (odd) variables $\theta$ and $\bar\theta$ of the Grassmann algebra. The Minkowski spacetime manifold, hidden in the supermanifold and parametrized by $x^\mu (\mu = 0, 1)$, is chosen to be a flat manifold on which a two $(1 + 1)$-dimensional (2D) free Abelian gauge theory, taken as a prototype field theoretical model, is defined. We demonstrate the applications of the above definition (and its further generalization) for the discussion of the (anti-)co-BRST symmetries that exist for the field theoretical models of 2D- (and 4D) free Abelian gauge theories considered on the four $(2 + 2)$- (and six $(4 + 2)$)-dimensional supermanifolds, respectively.Comment: LaTeX file, 25 pages, Journal-versio

Abelian 2-form gauge theory: superfield formalism

We derive the off-shell nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for {\it 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^\mu (with \mu = 0, 1, 2, 3) and a pair of odd Grassmannian variables \theta and \bar\theta (with \theta^2 = \bar\theta^2 = 0, \theta \bar\theta + \bar\theta \theta = 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.Comment: LaTeX file, 23 pages, journal versio

Constraints on the three-fluid model of curvaton decay

A three fluid system describing the decay of the curvaton is studied by numerical and analytical means. We place constraints on the allowed interaction strengths between the fluids and initial curvaton density by requiring that the curvaton decays before nucleosynthesis while nucleosynthesis, radiation-matter equality and decoupling occur at correct temperatures. We find that with a continuous, time-independent interaction, a small initial curvaton density is naturally preferred along with a low reheating temperature. Allowing for a time-dependent interaction, this constraint can be relaxed. In both cases, a purely adiabatic final state can be generated, but not without fine-tuning. Unlike in the two fluid system, the time-dependent interactions are found to have a small effect on the curvature perturbation itself due to the different nature of the system. The presence of non-gaussianity in the model is discussed.Comment: 9 pages, 10 figure