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

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

An Alternative To The Horizontality Condition In Superfield Approach To BRST Symmetries

We provide an alternative to the gauge covariant horizontality condition which is responsible for the derivation of the nilpotent (anti-)BRST symmetry transformations for the gauge and (anti-)ghost fields of a (3 + 1)-dimensional (4D) interacting 1-form non-Abelian gauge theory in the framework of the usual superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism. The above covariant horizontality condition is replaced by a gauge invariant restriction on the (4, 2)-dimensional supermanifold, parameterized by a set of four spacetime coordinates x^\mu (\mu = 0, 1, 2, 3) and a pair of Grassmannian variables \theta and \bar\theta. The latter condition enables us to derive the nilpotent (anti-)BRST symmetry transformations for all the fields of an interacting 4D 1-form non-Abelian gauge theory where there is an explicit coupling between the gauge field and the Dirac fields. The key differences and striking similarities between the above two conditions are pointed out clearly.Comment: LaTeX file, 20 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

Application of using Hybrid Renewable Energy in Saudi Arabia

One of the major world wide concerns of the utilities is to reduce the emissions from traditional power plants by using renewable energy and to reduce the high cost of supplying electricity to remote areas. Hybrid power systems can provide a good solution for such problems because they integrate renewable energy along with the traditional power plants. In Kingdom of Saudi Arabia a remote village called Al-Qtqt, was selected as a case study in order to investigate the ability to use a hybrid power system to provide the village with its needs of electricity. The simulation of this hybrid power system was done using HOMER software

Augmented Superfield Approach To Unique Nilpotent Symmetries For Complex Scalar Fields In QED

The derivation of the exact and unique nilpotent Becchi-Rouet-Stora-Tyutin (BRST)- and anti-BRST symmetries for the matter fields, present in any arbitrary interacting gauge theory, has been a long-standing problem in the framework of superfield approach to BRST formalism. These nilpotent symmetry transformations are deduced for the four (3 + 1)-dimensional (4D) complex scalar fields, coupled to the U(1) gauge field, in the framework of augmented superfield formalism. This interacting gauge theory (i.e. QED) is considered on a six (4, 2)-dimensional supermanifold parametrized by four even spacetime coordinates and a couple of odd elements of the Grassmann algebra. In addition to the horizontality condition (that is responsible for the derivation of the exact nilpotent symmetries for the gauge field and the (anti-)ghost fields), a new restriction on the supermanifold, owing its origin to the (super) covariant derivatives, has been invoked for the derivation of the exact nilpotent symmetry transformations for the matter fields. The geometrical interpretations for all the above nilpotent symmetries are discussed, too.Comment: LaTeX file, 17 pages, journal versio

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

A simplified structure for the second order cosmological perturbation equations

Increasingly accurate observations of the cosmic microwave background and the large scale distribution of galaxies necessitate the study of nonlinear perturbations of Friedmann-Lemaitre cosmologies, whose equations are notoriously complicated. In this paper we present a new derivation of the governing equations for second order perturbations within the framework of the metric-based approach that is minimal, as regards amount of calculation and length of expressions, and flexible, as regards choice of gauge and stress-energy tensor. Because of their generality and the simplicity of their structure our equations provide a convenient starting point for determining the behaviour of nonlinear perturbations of FL cosmologies with any given stress-energy content, using either the Poisson gauge or the uniform curvature gauge.Comment: 30 pages, no figures. Changed title to the one in published version and some minor changes and addition

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'

Large-scale structure and the redshift-distance relation

In efforts to demonstrate the linear Hubble law v = Hr from galaxy observations, the underlying simplicity is often obscured by complexities arising from magnitude-limited data. In this paper we point out a simple but previously unremarked fact: that the shapes and orientations of structures in redshift space contain in themselves independent information about the cosmological redshift-distance relation. The orientations of voids in the CfA slice support the Hubble law, giving a redshift-distance power index p = 0.83 +/- 0.36 (void data from Slezak, de Lapparent, & Bijoui 1993) or p = 0.99 +/- 0.38 (void data from Malik & Subramanian 1997).Comment: 11 pages (AASTeX), 4 figures, to appear in the Astrophysical Journal Letter