21,832 research outputs found
Boussinesq-type equations from nonlinear realizations of
We construct new coset realizations of infinite-dimensional linear
symmetry associated with Zamolodchikov's algebra which are
different from the previously explored Toda realization of
. We deduce the Boussinesq and modified Boussinesq equations as
constraints on the geometry of the corresponding coset manifolds.The main
characteristic features of these realizations are:i. Among the coset parameters
there are the space and time coordinates and which enter the Boussinesq
equations, all other coset parameters are regarded as fields depending on these
coordinates;ii. The spin 2 and 3 currents of and two spin 1 Kac-
Moody currents as well as two spin 0 fields related to the currents via
Miura maps, come out as the only essential parameters-fields of these cosets.
The remaining coset fields are covariantly expressed through them;iii.The Miura
maps get a new geometric interpretation as covariant constraints
which relate the above fields while passing from one coset manifold to another;
iv. The Boussinesq equation and two kinds of the modified Boussinesq equations
appear geometrically as the dynamical constraints accomplishing
covariant reductions of original coset manifolds to their two-dimensional
geodesic submanifolds;v. The zero-curvature representations for these equations
arise automatically as a consequence of the covariant reduction. The approach
proposed could provide a universal geometric description of the relationship
between -type algebras and integrable hierarchies.Comment: 23 pages, LaTe
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
N=2 Super - Algebra and N=2 Super Boussinesq Equations
We study classical super- algebra and its interplay with
supersymmetric extensions of the Boussinesq equation in the framework of the
nonlinear realization method and the inverse Higgs - covariant reduction
approach. These techniques have been previously applied by us in the bosonic
case to give a new geometric interpretation of the Boussinesq hierarchy.
Here we deduce the most general super Boussinesq equation and two kinds
of the modified super Boussinesq equations, as well as the super Miura
maps relating these systems to each other, by applying the covariant reduction
to certain coset manifolds of linear super- symmetry
associated with super-. We discuss the integrability properties of
the equations obtained and their correspondence with the formulation based on
the notion of the second hamiltonian structure.Comment: LaTeX, 30
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'
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
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
Hamiltonian and Lagrangian Dynamics in a Noncommutative Space
We discuss the dynamics of a particular two-dimensional (2D) physical system
in the four dimensional (4D) (non-)commutative phase space by exploiting the
consistent Hamiltonian and Lagrangian formalisms based on the symplectic
structures defined on the 4D (non-)commutative cotangent manifolds. The
noncommutativity exists {\it equivalently} in the coordinate or the momentum
planes embedded in the 4D cotangent manifolds. The signature of this
noncommutativity is reflected in the derivation of the first-order Lagrangians
where we exploit the most general form of the Legendre transformation defined
on the (non-)commutative (co-)tangent manifolds. The second-order Lagrangian,
defined on the 4D {\it tangent manifold}, turns out to be the {\it same}
irrespective of the noncommutativity present in the 4D cotangent manifolds for
the discussion of the Hamiltonian formulation. A connection with the
noncommutativity of the dynamics, associated with the quantum groups on the
q-deformed 4D cotangent manifolds, is also pointed out.Comment: LaTeX, 12 pages, minor changes in the title and text, references
expanded, version to appear in Mod. Phys. Lett.
Characterization and snubbing of a bidirectional MCT in a resonant ac link converter
The MOS-Controlled Thyristor (MCT) is emerging as a powerful switch that combines the better characteristics of existing power devices. A study of switching stresses on an MCT switch under zero voltage resonant switching is presented. The MCT is used as a bidirectional switch in an ac/ac pulse density modulated inverter for induction motor drive. Current and voltage spikes are observed and analyzed with variations in the timing of the switching. Different snubber circuit configurations are under investigation to minimize the effect of these transients. The results will be extended to study and test the MCT switching in a medium power (5 hp) induction motor drive
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