23,223 research outputs found
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'
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'
The basic cohomology of the twisted N=16, D=2 super Maxwell theory
We consider a recently proposed two-dimensional Abelian model for a Hodge
theory, which is neither a Witten type nor a Schwarz type topological theory.
It is argued that this model is not a good candidate for a Hodge theory since,
on-shell, the BRST Laplacian vanishes. We show, that this model allows for a
natural extension such that the resulting topological theory is of Witten type
and can be identified with the twisted N=16, D=2 super Maxwell theory.
Furthermore, the underlying basic cohomology preserves the Hodge-type structure
and, on-shell, the BRST Laplacian does not vanish.Comment: 9 pages, Latex; new Section 4 showing the invariants added; 2
references and relating remarks adde
Directional instability of microtubule transport in the presence of kinesin and dynein, two opposite polarity motor proteins.
Kinesin and dynein are motor proteins that move in opposite directions along microtubules. In this study, we examine the consequences of having kinesin and dynein (ciliary outer arm or cytoplasmic) bound to glass surfaces interacting with the same microtubule in vitro. Although one might expect a balance of opposing forces to produce little or no net movement, we find instead that microtubules move unidirectionally for several microns (corresponding to hundreds of ATPase cycles by a motor) but continually switch between kinesin-directed and dynein-directed transport. The velocities in the plus-end (0.2-0.3 microns/s) and minus-end (3.5-4 microns/s) directions were approximately half those produced by kinesin (0.5 microns/s) and ciliary dynein (6.7 microns/s) alone, indicating that the motors not contributing to movement can interact with and impose a drag upon the microtubule. By comparing two dyneins with different duty ratios (percentage of time spent in a strongly bound state during the ATPase cycle) and varying the nucleotide conditions, we show that the microtubule attachment times of the two opposing motors as well as their relative numbers determine which motor predominates in this assay. Together, these findings are consistent with a model in which kinesin-induced movement of a microtubule induces a negative strain in attached dyneins which causes them to dissociate before entering a force-generating state (and vice versa); reversals in the direction of transport may require the temporary dissociation of the transporting motor from the microtubule. The bidirectional movements described here are also remarkably similar to the back-and-forth movements of chromosomes during mitosis and membrane vesicles in fibroblasts. These results suggest that the underlying mechanical properties of motor proteins, at least in part, may be responsible for reversals in microtubule-based transport observed in cells
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
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
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
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
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