950 research outputs found
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
Rigid Rotor as a Toy Model for Hodge Theory
We apply the superfield approach to the toy model of a rigid rotor and show
the existence of the nilpotent and absolutely anticommuting
Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations, under
which, the kinetic term and action remain invariant. Furthermore, we also
derive the off-shell nilpotent and absolutely anticommuting (anti-) co-BRST
symmetry transformations, under which, the gauge-fixing term and Lagrangian
remain invariant. The anticommutator of the above nilpotent symmetry
transformations leads to the derivation of a bosonic symmetry transformation,
under which, the ghost terms and action remain invariant. Together, the above
transformations (and their corresponding generators) respect an algebra that
turns out to be a physical realization of the algebra obeyed by the de Rham
cohomological operators of differential geometry. Thus, our present model is a
toy model for the Hodge theory.Comment: LaTeX file, 22 page
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
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
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
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
Free Abelian 2-Form Gauge Theory: BRST Approach
We discuss various symmetry properties of the Lagrangian density of a four (3
+ 1)-dimensional (4D) free Abelian 2-form gauge theory within the framework of
Becchi-Rouet-Stora-Tyutin (BRST) formalism. The present free Abelian gauge
theory is endowed with a Curci-Ferrari type condition which happens to be a key
signature of the 4D non-Abelian 1-form gauge theory. In fact, it is due to the
above condition that the nilpotent BRST and anti-BRST symmetries of the theory
are found to be absolutely anticommuting in nature. For our present 2-form
gauge theory, we discuss the BRST, anti-BRST, ghost and discrete symmetry
properties of the Lagrangian densities and derive the corresponding conserved
charges. The algebraic structure, obeyed by the above conserved charges, is
deduced and the constraint analysis is performed with the help of the
physicality criteria where the conserved and nilpotent (anti-)BRST charges play
completely independent roles. These physicality conditions lead to the
derivation of the above Curci-Ferrari type restriction, within the framework of
BRST formalism, from the constraint analysis.Comment: LaTeX file, 21 pages, journal referenc
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
A field-theoretic model for Hodge theory
We demonstrate that the four (3 + 1)-dimensional free Abelian 2-form gauge
theory presents a tractable field theoretical model for the Hodge theory where
the well-defined symmetry transformations correspond to the de Rham
cohomological operators of differential geometry. The conserved charges,
corresponding to the above continuous symmetry transformations, obey an algebra
that is reminiscent of the algebra obeyed by the cohomological operators. The
discrete symmetry transformation of the theory represents the realization of
the Hodge duality operation that exists in the relationship between the
exterior and co-exterior derivatives of differential geometry. Thus, we provide
the realizations of all the mathematical quantities, associated with the de
Rham cohomological operators, in the language of the symmetries of the present
4D free Abelian 2-form gauge theory.Comment: LaTeX file, 24 pages, journal reference is give
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