Unique Nilpotent Symmetry Transformations For Matter Fields In QED: Augmented Superfield Formalism

We derive the local, covariant, continuous, anticommuting and off-shell nilpotent (anti-)BRST symmetry transformations for the interacting U(1) gauge theory of quantum electrodynamics (QED) in the framework of augmented superfield approach to BRST formalism. In addition to the horizontality condition, we invoke another gauge invariant condition on the six (4, 2)-dimensional supermanifold to obtain the exact and unique nilpotent symmetry transformations for all the basic fields, present in the (anti-)BRST invariant Lagrangian density of the physical four (3 + 1)-dimensional QED. The above supermanifold is parametrized by four even spacetime variables x^\mu (with \mu = 0, 1, 2, 3) and a couple of odd variables (\theta and \bar\theta) of the Grassmann algebra. The new gauge invariant condition on the supermanifold owes its origin to the (super) covariant derivatives and leads to the derivation of unique nilpotent symmetry transformations for the matter fields. The geometrical interpretations for all the above off-shell nilpotent transformations are discussed, too.Comment: LaTeX file, 14 pages, journal-versio

Nilpotent Symmetries For A Spinning Relativistic Particle In Augmented Superfield Formalism

The local, covariant, continuous, anticommuting and nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for all the fields of a (0 + 1)-dimensional spinning relativistic particle are obtained in the framework of augmented superfield approach to BRST formalism. The trajectory of this super-particle is parametrized by a monotonically increasing parameter \tau that is embedded in a D-dimensional flat Minkowski spacetime manifold. This physically useful one-dimensional system is considered on a three (1 + 2)-dimensional supermanifold which is parametrized by an even element \tau and a couple of odd elements \theta and \bar\theta of the Grassmann algebra. Two anticommuting sets of (anti-)BRST symmetry transformations, corresponding to the underlying (super)gauge symmetries for the above system, are derived in the framework of augmented superfield formulation where (i) the horizontality condition, and (ii) the invariance of conserved quantities on the supermanifold, play decisive roles. Geometrical interpretations for the above nilpotent symmetries (and their generators) are provided.Comment: LaTeX file, 21 pages, a notation clarified, a footnote added and related statements corrected in Introduction, version to appear in EPJ

Nilpotent Symmetries for QED in Superfield Formalism

In the framework of superfield approach, we derive the local, covariant, continuous and nilpotent (anti-)BRST and (anti-)co-BRST symmetry transformations on the U(1) gauge field $(A_\mu)$ and the (anti-)ghost fields $((\bar C)C)$ of the Lagrangian density of the two $(1 + 1)$-dimensional QED by exploiting the (dual-)horizontality conditions defined on the four $(2 + 2)$-dimensional supermanifold. The long-standing problem of the derivation of the above symmetry transformations for the matter (Dirac) fields $(\bar\psi, \psi)$ in the framework of superfield formulation is resolved by a new set of restrictions on the $(2 + 2)$-dimensional supermanifold. These new physically interesting restrictions on the supermanifold owe their origin to the invariance of conserved currents of the theory. The geometrical interpretation for all the above transformations is provided in the framework of superfield formalism.Comment: LaTeX file, 12 pages, title slightly changed, text altered, typos corrected, minor changes in equations (3.1), (3.7), (3.8) and (3.9), journal-ref give

Augmented Superfield Approach To Exact Nilpotent Symmetries For Matter Fields In Non-Abelian Theory

We derive the nilpotent (anti-)BRST symmetry transformations for the Dirac (matter) fields of an interacting four (3+1)-dimensional 1-form non-Abelian gauge theory by applying the theoretical arsenal of augmented superfield formalism where (i) the horizontality condition, and (ii) the equality of a gauge invariant quantity, on the six (4, 2)-dimensional supermanifold, are exploited together. The above supermanifold is parameterized by four bosonic spacetime coordinates x^\mu (with \mu = 0,1,2,3) and a couple of Grassmannian variables \theta and \bar{\theta}. The on-shell nilpotent BRST symmetry transformations for all the fields of the theory are derived by considering the chiral superfields on the five (4, 1)-dimensional super sub-manifold and the off-shell nilpotent symmetry transformations emerge from the consideration of the general superfields on the full six (4, 2)-dimensional supermanifold. Geometrical interpretations for all the above nilpotent symmetry transformations are also discussed in the framework of augmented superfield formalism.Comment: LaTeX file, 19 pages, journal-versio

Modular control-loop detection

This paper presents an efficient algorithm to detect control-loops in large finite-state systems. The proposed algorithm exploits the modular structure present in many models of practical relevance, and often successfully avoids the explicit synchronous composition of subsystems and thereby the state explosion problem. Experimental results show that the method can be used to verify industrial applications of considerable complexity

Novel symmetries in N = 2 supersymmetric quantum mechanical models

We demonstrate the existence of a novel set of discrete symmetries in the context of N = 2 supersymmetric (SUSY) quantum mechanical model with a potential function f(x) that is a generalization of the potential of the 1D SUSY harmonic oscillator. We perform the same exercise for the motion of a charged particle in the X-Y plane under the influence of a magnetic field in the Z-direction. We derive the underlying algebra of the existing continuous symmetry transformations (and corresponding conserved charges) and establish its relevance to the algebraic structures of the de Rham cohomological operators of differential geometry. We show that the discrete symmetry transformations of our present general theories correspond to the Hodge duality operation. Ultimately, we conjecture that any arbitrary N = 2 SUSY quantum mechanical system can be shown to be a tractable model for the Hodge theory.Comment: LaTeX file, 23 pages, Title and Abstract changed, Text modified, version to appear in Annals of Physic

The basic cohomology of the twisted N=16, D=2 super Maxwell theory

We consider a recently proposed two-dimensional Abelian model for a Hodge theory, which is neither a Witten type nor a Schwarz type topological theory. It is argued that this model is not a good candidate for a Hodge theory since, on-shell, the BRST Laplacian vanishes. We show, that this model allows for a natural extension such that the resulting topological theory is of Witten type and can be identified with the twisted N=16, D=2 super Maxwell theory. Furthermore, the underlying basic cohomology preserves the Hodge-type structure and, on-shell, the BRST Laplacian does not vanish.Comment: 9 pages, Latex; new Section 4 showing the invariants added; 2 references and relating remarks adde

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

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