Superfield approach to a novel symmetry for non-Abelian gauge theory

In the framework of superfield formalism, we demonstrate the existence of a new local, covariant, continuous and nilpotent (dual-BRST) symmetry for the BRST invariant Lagrangian density of a self-interacting two ($1 + 1$)-dimensional (2D) non-Abelian gauge theory (having no interaction with matter fields). The local and nilpotent Noether conserved charges corresponding to the above continuous symmetries find their geometrical interpretation as the translation generators along the odd (Grassmannian) directions of the four ($2 + 2)$-dimensional supermanifold.Comment: LaTeX, 12 pages, equations (4.2)--(4.6) correcte

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

The changing role of house price dynamics over the business cycle

In this paper, we attempt to analyse the relationship between house price developments and the business cycle. Employing a time-varying transition probability Markov switching framework, we provide empirical evidence that house price growth may prove a useful leading indicator for turning point detection. In focusing on three countries, the US, UK and Spain, we furthermore provide evidence that although potentially informative from an overall perspective in business cycle modelling, the signi.cance of signals contained in house prices may not be symmetric across the identi.ed high growth and low growth states. In addition, we suggest a possible range of values for house price de.ation which may trigger a recession the following period.Business cycles, leading indicators, housing, Markov switching.

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

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

Topological aspects in non-Abelian gauge theory

We discuss the BRST cohomology and exhibit a connection between the Hodge decomposition theorem and the topological properties of a two dimensional free non-Abelian gauge theory having no interaction with matter fields. The topological nature of this theory is encoded in the vanishing of the Laplacian operator when equations of motion are exploited. We obtain two sets of topological invariants with respect to BRST and co-BRST charges on the two dimensional manifold and show that the Lagrangian density of the theory can be expressed as the sum of terms that are BRST- and co-BRST invariants.Comment: (1+11) pages, LaTeX, no figure

Supersymmetrization of horizontality condition: nilpotent symmetries for a free spinning relativistic particle

We derive the off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for a supersymmetric system of a free spinning relativistic particle within the framework of superfield approach to BRST formalism. A novel feature of our present investigation is the consistent and clear supersymmetric modification of the celebrated horizontality condition for the precise determination of the proper (anti-)BRST symmetry transformations for all the bosonic and fermionic dynamical variables of our theory which is considered on a (1, 2)-dimensional supermanifold parameterized by an even (bosonic) variable (\tau) and a pair of odd (fermionic) variables \theta and \bar\theta (with \theta^2 = \bar\theta^2 = 0,\; \theta \bar\theta + \bar\theta \theta = 0) of the Grassmann algebra. One of the most important features of our present investigation is the derivation of (anti-)BRST invariant Curci-Ferrari type restriction which turns out to be responsible for the absolute anticommutativity of the (anti-)BRST symmetry transformations and existence of the coupled (but equivalent) Lagrangians for the present theory of a supersymmetric system.Comment: LaTeX file, 24 pages, version to appear in EPJ