27,147 research outputs found
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'
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 -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
BRST cohomology and Hodge decomposition theorem in Abelian gauge theory
We discuss the Becchi-Rouet-Stora-Tyutin (BRST) cohomology and Hodge
decomposition theorem for the two dimensional free U(1) gauge theory. In
addition to the usual BRST charge, we derive a local, conserved and nilpotent
co(dual)-BRST charge under which the gauge-fixing term remains invariant. We
express the Hodge decomposition theorem in terms of these charges and the
Laplacian operator. We take a single photon state in the quantum Hilbert space
and demonstrate the notion of gauge invariance, no-(anti)ghost theorem,
transversality of photon and establish the topological nature of this theory by
exploiting the concepts of BRST cohomology and Hodge decomposition theorem. In
fact, the topological nature of this theory is encoded in the vanishing of the
Laplacian operator when equations of motion are exploited. On the two
dimensional compact manifold, we derive two sets of topological invariants with
respect to the conserved and nilpotent BRST- and co-BRST charges and express
the Lagrangian density of the theory as the sum of terms that are BRST- and
co-BRST invariants. Mathematically, this theory captures together some of the
key features of both Witten- and Schwarz type of topological field theories.Comment: 20 pages, LaTeX, no figures, Title and text have been changed,
Journal reference is given, some references have been adde
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 -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
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'
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
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 ()-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 (-dimensional supermanifold.Comment: LaTeX, 12 pages, equations (4.2)--(4.6) correcte
Nilpotent (anti-)BRST symmetry transformations for dynamical non-Abelian 2-form gauge theory: superfield formalism
We derive the off-shell nilpotent and absolutely anticommuting
Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the
dynamical non-Abelian 2-form gauge theory within the framework of geometrical
superfield formalism. We obtain the (anti-) BRST invariant coupled Lagrangian
densities that respect the above nilpotent symmetry transformations. We
discuss, furthermore, this (anti-) BRST invariance in the language of the
superfield formalism. One of the novel features of our investigation is the
observation that, in addition to the horizontality condition, we have to invoke
some other physically relevant restrictions to deduce the exact (anti-) BRST
symmetry transformations for all the fields of the topologically massive
non-Abelian gauge theory.Comment: LaTeX file, 8 pages, typos fixed in some equations, journal-versio
- …