4,730 research outputs found
The Schwinger SU(3) construction - I: Multiplicity problem and relation to induced representations
The Schwinger oscillator operator representation of SU(3) is analysed with
particular reference to the problem of multiplicity of irreducible
representations. It is shown that with the use of an unitary
representation commuting with the SU(3) representation, the infinity of
occurrences of each SU(3) irreducible representation can be handled in complete
detail. A natural `generating representation' for SU(3), containing each
irreducible representation exactly once, is identified within a subspace of the
Schwinger construction; and this is shown to be equivalent to an induced
representation of SU(3).Comment: Latex, 25 page
BRST quantization of matrix models with constraints and two-dimensional Yang-Mills theory on the cylinder
BRST quantization of the one-dimensional constrained matrix model which
describes two-dimensional Yang-Mills theory on the cylinder is performed.
Classical and quantum BRST generators and BRST-invariant hamiltonians are
constructed. Evolution operator is expressed in terms of BRST path integral.
Advantages of the BRST quantization over the reduced phase space approach
leading to the theory of free fermions are discussed.Comment: 8 page
Noncommutative symmetric functions and Laplace operators for classical Lie algebras
New systems of Laplace (Casimir) operators for the orthogonal and symplectic
Lie algebras are constructed. The operators are expressed in terms of paths in
graphs related to matrices formed by the generators of these Lie algebras with
the use of some properties of the noncommutative symmetric functions associated
with a matrix. The decomposition of the Sklyanin determinant into a product of
quasi-determinants play the main role in the construction. Analogous
decomposition for the quantum determinant provides an alternative proof of the
known construction for the Lie algebra gl(N).Comment: 25 page
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The Chandrayaan-2 Large Area Soft X-ray Spectrometer (CLASS)
The CLASS experiment on Chandrayaan-2, the second Indian lunar mission, aims tomap the abundance of the major rock forming elements on the lunar surface using the technique of X-ray fluorescence during solar flare events. CLASS is a continuation of the successful C1XS [1] XRF experiment on Chandrayaan-1. CLASS is designed to provide lunar mapping of elemental abundances with a nominal spatial resolution of 25 km (FWHM) from a 200 km polar, circular orbit of Chandrayaan-2
Einstein-Weyl structures and Bianchi metrics
We analyse in a systematic way the (non-)compact four dimensional
Einstein-Weyl spaces equipped with a Bianchi metric. We show that Einstein-Weyl
structures with a Class A Bianchi metric have a conformal scalar curvature of
constant sign on the manifold. Moreover, we prove that most of them are
conformally Einstein or conformally K\"ahler ; in the non-exact Einstein-Weyl
case with a Bianchi metric of the type or , we show that the
distance may be taken in a diagonal form and we obtain its explicit
4-parameters expression. This extends our previous analysis, limited to the
diagonal, K\"ahler Bianchi case.Comment: Latex file, 12 pages, a minor modification, accepted for publication
in Class. Quant. Gra
Degenerate principal series of quantum Harish-Chandra modules
In this paper we study a quantum analogue of a degenerate principal series of
-modules () related to the Shilov boundary of
the quantum -matrix unit ball. We give necessary and sufficient
conditions for the modules to be simple and unitarizable and investigate their
equivalence.
These results are q-analogues of known classical results on reducibility and
unitarizability of SU(n,n)-modules obtained by Johnson, Sahi, Zhang, Howe and
Tan.Comment: 33 pages, 4 figure
Conformal and Superconformal Mechanics
We investigate the conformal and superconformal properties of a
non-relativistic spinning particle propagating in a curved background coupled
to a magnetic field and with a scalar potential. We derive the conditions on
the couplings for a large class of such systems which are necessary in order
their actions admit conformal and superconformal symmetry. We find that some of
these conditions can be encoded in the conformal and holomorphic geometry of
the background. Several new examples of conformal and superconformal models are
also given.Comment: 46 pages, Phyzzx.te
Ultrafast control of inelastic tunneling in a double semiconductor quantum
In a semiconductor-based double quantum well (QW) coupled to a degree of
freedom with an internal dynamics, we demonstrate that the electronic motion is
controllable within femtoseconds by applying appropriately shaped
electromagnetic pulses. In particular, we consider a pulse-driven AlxGa1-xAs
based symmetric double QW coupled to uniformly distributed or localized
vibrational modes and present analytical results for the lowest two levels.
These predictions are assessed and generalized by full-fledged numerical
simulations showing that localization and time-stabilization of the driven
electron dynamics is indeed possible under the conditions identified here, even
with a simultaneous excitations of vibrational modes.Comment: to be published in Appl.Phys.Let
Global analysis by hidden symmetry
Hidden symmetry of a G'-space X is defined by an extension of the G'-action
on X to that of a group G containing G' as a subgroup. In this setting, we
study the relationship between the three objects:
(A) global analysis on X by using representations of G (hidden symmetry);
(B) global analysis on X by using representations of G';
(C) branching laws of representations of G when restricted to the subgroup
G'.
We explain a trick which transfers results for finite-dimensional
representations in the compact setting to those for infinite-dimensional
representations in the noncompact setting when is -spherical.
Applications to branching problems of unitary representations, and to spectral
analysis on pseudo-Riemannian locally symmetric spaces are also discussed.Comment: Special volume in honor of Roger Howe on the occasion of his 70th
birthda
Dual Actions for Born-Infeld and Dp-Brane Theories
Dual actions with respect to U(1) gauge fields for Born-Infeld and -brane
theories are reexamined. Taking into account an additional condition, i.e. a
corollary to the field equation of the auxiliary metric, one obtains an
alternative dual action that does not involve the infinite power series in the
auxiliary metric given by ref. \cite{s14}, but just picks out the first term
from the series formally. New effective interactions of the theories are
revealed. That is, the new dual action gives rise to an effective interaction
in terms of one interaction term rather than infinite terms of different
(higher) orders of interactions physically. However, the price paid for
eliminating the infinite power series is that the new action is not quadratic
but highly nonlinear in the Hodge dual of a -form field strength. This
non-linearity is inevitable to the requirement the two dual actions are
equivalent.Comment: v1: 11 pages, no figures; v2: explanation of effective interactions
added; v3: concision made; v4: minor modification mad
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