17,845 research outputs found
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
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
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
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
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
Constraints on the three-fluid model of curvaton decay
A three fluid system describing the decay of the curvaton is studied by
numerical and analytical means. We place constraints on the allowed interaction
strengths between the fluids and initial curvaton density by requiring that the
curvaton decays before nucleosynthesis while nucleosynthesis, radiation-matter
equality and decoupling occur at correct temperatures. We find that with a
continuous, time-independent interaction, a small initial curvaton density is
naturally preferred along with a low reheating temperature. Allowing for a
time-dependent interaction, this constraint can be relaxed. In both cases, a
purely adiabatic final state can be generated, but not without fine-tuning.
Unlike in the two fluid system, the time-dependent interactions are found to
have a small effect on the curvature perturbation itself due to the different
nature of the system. The presence of non-gaussianity in the model is
discussed.Comment: 9 pages, 10 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
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'
Nilpotent Symmetries For Matter Fields In Non-Abelian Gauge Theory: Augmented Superfield Formalism
In the framework of superfield approach to Becchi-Rouet-Stora-Tyutin (BRST)
formalism, the derivation of the (anti-)BRST nilpotent symmetries for the
matter fields, present in any arbitrary interacting gauge theory, has been a
long-standing problem. In our present investigation, the local, covariant,
continuous and off-shell nilpotent (anti-)BRST symmetry transformations for the
Dirac fields are derived in the framework of the augmented
superfield formulation where the four -dimensional (4D) interacting
non-Abelian gauge theory is considered on the six -dimensional
supermanifold parametrized by the four even spacetime coordinates and a
couple of odd elements ( and ) of the Grassmann algebra.
The requirement of the invariance of the matter (super)currents and the
horizontality condition on the (super)manifolds leads to the derivation of the
nilpotent symmetries for the matter fields as well as the gauge- and the
(anti-)ghost fields of the theory in the general scheme of the augmented
superfield formalism.Comment: LaTeX file, 16 pages, printing mistakes in the second paragraph of
`Introduction' corrected, a footnote added, these modifications submitted as
``erratum'' to IJMPA in the final for
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'
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