17,609 research outputs found
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
Supersymmetric Oscillator: Novel Symmetries
We discuss various continuous and discrete symmetries of the supersymmetric
simple harmonic oscillator (SHO) in one (0 + 1)-dimension of spacetime and show
their relevance in the context of mathematics of differential geometry. We show
the existence of a novel set of discrete symmetries in the theory which has,
hitherto, not been discussed in the literature on theoretical aspects of SHO.
We also point out the physical relevance of our present investigation.Comment: REVTeX file, 5 pages, minor changes in title, text and abstract,
references expanded, version to appear in EP
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'
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
Numerical simulation of Goertler/Tollmien-Schlichting wave-interaction
The problem of nonlinear development of Goertler vortices and interaction with Tollmien-Schlichting (TS) waves is considered within the framework of incompressible Navier-Stokes equations which are solved by a Fourier-Chebyshev spectral method. It is shown that two-dimensional waves can be excited in the flow modulated by Goertler vortices. Due to nonlinear effects, this interaction further leads to the development of oblique waves with spanwise wavelength equal to the Goertler vortex wavelength. Interaction is also considered of oblique waves with spanwise wavelength twice that of Goertler vortices
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
Supersonic laminar-flow control
Detailed, up to date systems studies of the application of laminar flow control (LFC) to various supersonic missions and/or vehicles, both civilian and military, are not yet available. However, various first order looks at the benefits are summarized. The bottom line is that laminar flow control may allow development of a viable second generation SST. This follows from a combination of reduced fuel, structure, and insulation weight permitting operation at higher altitudes, thereby lowering sonic boom along with improving performance. The long stage lengths associated with the emerging economic importance of the Pacific Basin are creating a serious and renewed requirement for such a vehicle. Supersonic LFC techniques are discussed
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
On the receptivity and non-parallel stability of travelling disturbances in rotating disk flow
The generation and evolution of small amplitude wavelength traveling disturbances in rotating disk flow is discussed. The steady rotational speed of the disk is perturbed so as to introduce high frequency oscillations in the flow field. Secondly, surface imperfections are introduced on the disk such as roughness elements. The interaction of these two disturbances will generate the instability waves whose evolution is governed by parabolic partial differential equations that are solved numerically. For the class of disturbances considered (wavelength on the order of Reynolds number), it is found that eigensolutions exist which decay or grow algebraically in the radial direction. However, these solutions grow only for frequencies larger than 4.58 times the steady rotational speed of the disk. The computed receptivity coefficient shows that there is an optimum size of roughness for which these modes are excited the most. The width of these roughness elements in the radial direction is about .1 r(sub 0) where r(sub 0) is the radial location of the roughness. It is also found that the receptivity coefficient is larger for a negative spanwise wavenumber than for a positive one. Typical wave angles found for these disturbances are about -26 degrees
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