20,564 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'
A Concise Introduction to Perturbation Theory in Cosmology
We give a concise, self-contained introduction to perturbation theory in
cosmology at linear and second order, striking a balance between mathematical
rigour and usability. In particular we discuss gauge issues and the active and
passive approach to calculating gauge transformations. We also construct
gauge-invariant variables, including the second order tensor perturbation on
uniform curvature hypersurfaces.Comment: revtex4, 16 pages, 3 figures; v2: minor changes, typos corrected,
reference added, version accepted by CQ
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'
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
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 (Non-)local Symmetries for One-Form Abelian Gauge Theory
We exploit the geometrical superfield formalism to derive the local,
covariant and continuous Becchi-Rouet-Stora-Tyutin (BRST) symmetry
transformations and the non-local, non-covariant and continuous dual-BRST
symmetry transformations for the free Abelian one-form gauge theory in four -dimensions (4D) of spacetime. Our discussion is carried out in the
framework of BRST invariant Lagrangian density for the above 4D theory in the
Feynman gauge. The geometrical origin and interpretation for the (dual-)BRST
charges (and the transformations they generate) are provided in the language of
translations of some superfields along the Grassmannian directions of the six
(-dimensional supermanifold parametrized by the four spacetime and two
Grassmannian variables.Comment: LaTeX file, 23 page
Hodge Duality Operation And Its Physical Applications On Supermanifolds
An appropriate definition of the Hodge duality operation on any
arbitrary dimensional supermanifold has been a long-standing problem. We define
a working rule for the Hodge duality operation on the -dimensional supermanifold parametrized by a couple of even (bosonic)
spacetime variables and a couple of Grassmannian (odd)
variables and of the Grassmann algebra. The Minkowski
spacetime manifold, hidden in the supermanifold and parametrized by , is chosen to be a flat manifold on which a two -dimensional
(2D) free Abelian gauge theory, taken as a prototype field theoretical model,
is defined. We demonstrate the applications of the above definition (and its
further generalization) for the discussion of the (anti-)co-BRST symmetries
that exist for the field theoretical models of 2D- (and 4D) free Abelian gauge
theories considered on the four - (and six )-dimensional
supermanifolds, respectively.Comment: LaTeX file, 25 pages, Journal-versio
Evolution-guided functional analyses reveal diverse antiviral specificities encoded by IFIT1 genes in mammals.
IFIT (interferon-induced with tetratricopeptide repeats) proteins are critical mediators of mammalian innate antiviral immunity. Mouse IFIT1 selectively inhibits viruses that lack 2'O-methylation of their mRNA 5' caps. Surprisingly, human IFIT1 does not share this antiviral specificity. Here, we resolve this discrepancy by demonstrating that human and mouse IFIT1 have evolved distinct functions using a combination of evolutionary, genetic and virological analyses. First, we show that human IFIT1 and mouse IFIT1 (renamed IFIT1B) are not orthologs, but are paralogs that diverged >100 mya. Second, using a yeast genetic assay, we show that IFIT1 and IFIT1B proteins differ in their ability to be suppressed by a cap 2'O-methyltransferase. Finally, we demonstrate that IFIT1 and IFIT1B have divergent antiviral specificities, including the discovery that only IFIT1 proteins inhibit a virus encoding a cap 2'O-methyltransferase. These functional data, combined with widespread turnover of mammalian IFIT genes, reveal dramatic species-specific differences in IFIT-mediated antiviral repertoires
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
Cohomological aspects of Abelian gauge theory
We discuss some aspects of cohomological properties of a two-dimensional free
Abelian gauge theory in the framework of BRST formalism. We derive the
conserved and nilpotent BRST- and co-BRST charges and express the Hodge
decomposition theorem in terms of these charges and a conserved bosonic charge
corresponding to the Laplacian operator. It is because of the topological
nature of free U(1) gauge theory that the Laplacian operator goes to zero when
equations of motion are exploited. We derive two sets of topological invariants
which are related to each-other by a certain kind of duality transformation and
express the Lagrangian density of this theory as the sum of terms that are
BRST- and co-BRST invariants. Mathematically, this theory captures together
some of the key features of Witten- and Schwarz type of topological field
theories.Comment: 12 pages, LaTeX, no figures, Title and text have been slightly
changed, Journal reference is given and a reference has been adde
- …