18,658 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'
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
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
Abelian 2-form gauge theory: superfield formalism
We derive the off-shell nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and
anti-BRST symmetry transformations for {\it all} the fields of a free Abelian
2-form gauge theory by exploiting the geometrical superfield approach to BRST
formalism. The above four (3 + 1)-dimensional (4D) theory is considered on a
(4, 2)-dimensional supermanifold parameterized by the four even spacetime
variables x^\mu (with \mu = 0, 1, 2, 3) and a pair of odd Grassmannian
variables \theta and \bar\theta (with \theta^2 = \bar\theta^2 = 0, \theta
\bar\theta + \bar\theta \theta = 0). One of the salient features of our present
investigation is that the above nilpotent (anti-)BRST symmetry transformations
turn out to be absolutely anticommuting due to the presence of a Curci-Ferrari
(CF) type of restriction. The latter condition emerges due to the application
of our present superfield formalism. The actual CF condition, as is well-known,
is the hallmark of a 4D non-Abelian 1-form gauge theory. We demonstrate that
our present 4D Abelian 2-form gauge theory imbibes some of the key signatures
of the 4D non-Abelian 1-form gauge theory. We briefly comment on the
generalization of our supperfield approach to the case of Abelian 3-form gauge
theory in four (3 + 1)-dimensions of spacetime.Comment: LaTeX file, 23 pages, journal versio
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
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
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
Field Evaluations of Herbicides on Vegetable, Small Fruit, and Ornamental Crops, 2000, 2001, & 2002
Field evaluations of herbicides provide the chemical industry, governmental agencies, such as IR-4, and the Arkansas Agricultural Experiment Station with an evaluation of herbicide performance on small fruit, vegetable, and ornamental crops grown under Arkansas conditions. This report provides a means for disseminating information to interested private and public service weed scientists
Boundary layer transition
The boundary layer stability, its active control by sound and surface heating and the effect of curvature are studied numerically and experimentally for subsonic flow. In addition, the experimental and flight test data are correlated using the stability theory for supersonic Mach numbers. Active transition fixing and feedback control of boundary layer by sound interactions are experimentally investigated at low speed over an airfoil. Numerical simulation of active control by surface heating and cooling in air shows that by appropriate phase adjustment a reduction in the level of perturbation can be obtained. This simulation is based on the solution of two-dimensional compressible Navier-Stokes equations for a flat plate. Goertler vortices are studied experimentally on an airfoil in the Low Turbulence Pressure Tunnel (LTPT). The flow pattern was visualized using the sublimating chemical technique and data were obtained using a three component laser velocimeter. The effect of curvature on swept leading-edge stability on a cylinder was numerically studied. The results suggest that transition is dominated by traveling disturbance waves and that the waves with the greatest total amplification has an amplitude ratio of e sup 11. Experimental data from the quiet supersonic tunnel and flight tests are analyzed using linear compressible stability theory
Absolutely anticommuting (anti-)BRST symmetry transformations for topologically massive Abelian gauge theory
We demonstrate the existence of the nilpotent and absolutely anticommuting
Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the
four (3 + 1)-dimensional (4D) topologically massive Abelian U(1) gauge theory
that is described by the coupled Lagrangian densities (which incorporate the
celebrated (B \wedge F) term). The absolute anticommutativity of the (anti-)
BRST symmetry transformations is ensured by the existence of a Curci-Ferrari
type restriction that emerges from the superfield formalism as well as from the
equations of motion that are derived from the above coupled Lagrangian
densities. We show the invariance of the action from the point of view of the
symmetry considerations as well as superfield formulation. We discuss,
furthermore, the topological term within the framework of superfield formalism
and provide the geometrical meaning of its invariance under the (anti-) BRST
symmetry transformations.Comment: LaTeX file, 22 pages, journal versio
- …