16,510 research outputs found
(Anti-)chiral Superfield Approach to Nilpotent Symmetries: Self-Dual Chiral Bosonic Theory
We exploit the beauty and strength of the symmetry invariant restrictions on
the (anti-)chiral superfields to derive the Becchi-Rouet-Stora-Tyutin (BRST),
anti-BRST and (anti-)co-BRST symmetry transformations in the case of a two
(1+1)-dimensional (2D) self-dual chiral bosonic field theory within the
framework of augmented (anti-)chiral superfield formalism. Our 2D ordinary
theory is generalized onto a (2, 2)-dimensional supermanifold which is
parameterized by the superspace variable Z^M = (x^\mu, \theta, \bar\theta)
where x^\mu (with \mu = 0, 1) are the ordinary 2D bosonic coordinates and
(\theta,\, \bar\theta) are a pair of Grassmannian variables with their standard
relationships: \theta^2 = {\bar\theta}^2 =0, \theta\,\bar\theta +
\bar\theta\theta = 0. We impose the (anti-)BRST and (anti-)co-BRST invariant
restrictions on the (anti-)chiral superfields (defined on the (anti-)chiral (2,
1)-dimensional super-submanifolds of the above general (2, 2)-dimensional
supermanifold) to derive the above nilpotent symmetries. We do not exploit the
mathematical strength of the (dual-)horizontality conditions anywhere in our
present investigation. We also discuss the properties of nilpotency, absolute
anticommutativity and (anti-)BRST and (anti-)co-BRST symmetry invariance of the
Lagrangian density within the framework of our augmented (anti-)chiral
superfield formalism. Our observation of the absolute anticommutativity
property is a completely novel result in view of the fact that we have
considered only the (anti-)chiral superfields in our present endeavor.Comment: LaTeX file, 20 pages, journal reference is give
Superspace Unitary Operator in QED with Dirac and Complex Scalar Fields: Superfield Approach
We exploit the strength of the superspace (SUSP) unitary operator to obtain
the results of the application of the horizontality condition (HC) within the
framework of augmented version of superfield formalism that is applied to the
interacting systems of Abelian 1-form gauge theories where the U(1) Abelian
1-form gauge field couples to the Dirac and complex scalar fields in the
physical four (3 + 1)-dimensions of spacetime. These interacting theories are
generalized onto a (4, 2)-dimensional supermanifold that is parametrized by the
four (3 + 1)-dimensional (4D) spacetime variables and a pair of Grassmannian
variables. To derive the (anti-)BRST symmetries for the matter fields, we
impose the gauge invariant restrictions (GIRs) on the superfields defined on
the (4, 2)-dimensional supermanifold. We discuss various outcomes that emerge
out from our knowledge of the SUSP unitary operator and its hermitian
conjugate. The latter operator is derived without imposing any operation of
hermitian conjugation on the parameters and fields of our theory from outside.
This is an interesting observation in our present investigation.Comment: LaTeX file, 11 pages, journal versio
Self-Dual Chiral Boson: Augmented Superfield Approach
We exploit the standard tools and techniques of the augmented version of
Bonora-Tonin (BT) superfield formalism to derive the off-shell nilpotent and
absolutely anticommuting (anti-)BRST and (anti-)co-BRST symmetry
transformations for the Becchi-Rouet-Stora-Tyutin (BRST) invariant Lagrangian
density of a self-dual bosonic system. In the derivation of the full set of the
above transformations, we invoke the (dual-)horizontality conditions,
(anti-)BRST and (anti-)co-BRST invariant restrictions on the superfields that
are defined on the (2, 2)-dimensional supermanifold. The latter is
parameterized by the bosonic variable x^\mu\,(\mu = 0,\, 1) and a pair of
Grassmanian variables \theta and \bar\theta (with \theta^2 = \bar\theta^2 = 0
and \theta\bar\theta + \bar\theta\theta = 0). The dynamics of this system is
such that, instead of the full (2, 2) dimensional superspace coordinates
(x^\mu, \theta, \bar\theta), we require only the specific (1, 2)-dimensional
super-subspace variables (t, \theta, \bar\theta) for its description. This is a
novel observation in the context of superfield approach to BRST formalism. The
application of the dual-horizontality condition, in the derivation of a set of
proper (anti-)co-BRST symmetries, is also one of the new ingredients of our
present endeavor where we have exploited the augmented version of superfield
formalism which is geometrically very intuitive.Comment: LaTeX file, 27 pages, minor modifications, Journal reference is give
Curci-Ferrari Type Condition in Hamiltonian Formalism: A Free Spinning Relativistic Particle
The Curci-Ferrari (CF)-type of restriction emerges in the description of a
free spinning relativistic particle within the framework of
Becchi-Rouet-Stora-Tyutin (BRST) formalism when the off-shell nilpotent and
absolutely anticommuting (anti-)BRST symmetry transformations for this system
are derived from the application of horizontality condition (HC) and its
supersymmetric generalization (SUSY-HC) within the framework of superfield
formalism. We show that the above CF-condition, which turns out to be the
secondary constraint of our present theory, remains time-evolution invariant
within the framework of Hamiltonian formalism. This time-evolution invariance
(i) physically justifies the imposition of the (anti-)BRST invariant CF-type
condition on this system, and (ii) mathematically implies the linear
independence of BRST and anti-BRST symmetries of our present theory.Comment: LaTeX file, 11 Pages, journal versio
Superfield Approach To Nilpotent Symmetries For QED From A Single Restriction: An Alternative To The Horizontality Condition
We derive together the exact local, covariant, continuous and off-shell
nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry
transformations for the U(1) gauge field (A_\mu), the (anti-)ghost fields
((\bar C)C) and the Dirac fields (\psi, \bar\psi) of the Lagrangian density of
a four (3 + 1)-dimensional QED by exploiting a single restriction on the six
(4, 2)-dimensional supermanifold. A set of four even spacetime coordinates
x^\mu (\mu = 0, 1, 2, 3) and two odd Grassmannian variables \theta and
\bar\theta parametrize this six dimensional supermanifold. The new gauge
invariant restriction on the above supermanifold owes its origin to the (super)
covariant derivatives and their intimate relations with the (super) 2-form
curvatures (\tilde F^{(2)})F^{(2)} constructed with the help of (super) 1-form
gauge connections (\tilde A^{(1)})A^{(1)} and (super) exterior derivatives
(\tilde d)d. The results obtained separately by exploiting (i) the
horizontality condition, and (ii) one of its consistent extensions, are shown
to be a simple consequence of this new single restriction on the above
supermanifold. Thus, our present endeavour provides an alternative to (and, in
some sense, generalization of) the horizontality condition of the usual
superfield formalism applied to the derivation of BRST symmetries.Comment: LaTeX file, 15 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
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
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
Normal mode splitting and mechanical effects of an optical lattice in a ring cavity
A novel regime of atom-cavity physics is explored, arising when large atom
samples dispersively interact with high-finesse optical cavities. A stable far
detuned optical lattice of several million rubidium atoms is formed inside an
optical ring resonator by coupling equal amounts of laser light to each
propagation direction of a longitudinal cavity mode. An adjacent longitudinal
mode, detunedby about 3 GHz, is used to perform probe transmission spectroscopy
of the system. The atom-cavity coupling for the lattice beams and the probe is
dispersive and dissipation results only from the finite photon-storage time.
The observation of two well-resolved normal modes demonstrates the regime of
strong cooperative coupling. The details of the normal mode spectrum reveal
mechanical effects associated with the retroaction of the probe upon the
optical lattice.Comment: 4 pages, 3 figure
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