656 research outputs found
Geometric quantization on homogeneous spaces and the meaning of `inequivalent' quantizations
Consideration of the geometric quantization of the phase space of a particle
in an external Yang-Mills field allows the results of the Mackey-Isham
quantization procedure for homogeneous configuration spaces to be
reinterpreted. In particular, a clear physical interpretation of the
`inequivalent' quantizations occurring in that procedure is given.Comment: 8 page
Symplectic structures associated to Lie-Poisson groups
The Lie-Poisson analogues of the cotangent bundle and coadjoint orbits of a
Lie group are considered. For the natural Poisson brackets the symplectic
leaves in these manifolds are classified and the corresponding symplectic forms
are described. Thus the construction of the Kirillov symplectic form is
generalized for Lie-Poisson groups.Comment: 30 page
Dual Isomonodromic Deformations and Moment Maps to Loop Algebras
The Hamiltonian structure of the monodromy preserving deformation equations
of Jimbo {\it et al } is explained in terms of parameter dependent pairs of
moment maps from a symplectic vector space to the dual spaces of two different
loop algebras. The nonautonomous Hamiltonian systems generating the
deformations are obtained by pulling back spectral invariants on Poisson
subspaces consisting of elements that are rational in the loop parameter and
identifying the deformation parameters with those determining the moment maps.
This construction is shown to lead to ``dual'' pairs of matrix differential
operators whose monodromy is preserved under the same family of deformations.
As illustrative examples, involving discrete and continuous reductions, a
higher rank generalization of the Hamiltonian equations governing the
correlation functions for an impenetrable Bose gas is obtained, as well as dual
pairs of isomonodromy representations for the equations of the Painleve
transcendents and .Comment: preprint CRM-1844 (1993), 28 pgs. (Corrected date and abstract.
g_{rho sigma gamma} coupling constant in light cone QCD
The coupling constant g_{rho sigma gamma} is determined from light cone QCD
sum rules. A comparison of our result with the ones existing in literature is
presented.Comment: 7 pp, 2 figures (postscript formatted), LaTex formatte
More on quantum groups from the the quantization point of view
Star products on the classical double group of a simple Lie group and on
corresponding symplectic grupoids are given so that the quantum double and the
"quantized tangent bundle" are obtained in the deformation description.
"Complex" quantum groups and bicovariant quantum Lie algebras are discused from
this point of view. Further we discuss the quantization of the Poisson
structure on symmetric algebra leading to the quantized enveloping
algebra as an example of biquantization in the sense of Turaev.
Description of in terms of the generators of the bicovariant
differential calculus on is very convenient for this purpose. Finally
we interpret in the deformation framework some well known properties of compact
quantum groups as simple consequences of corresponding properties of classical
compact Lie groups. An analogue of the classical Kirillov's universal character
formula is given for the unitary irreducible representation in the compact
case.Comment: 18 page
Meson model for f_0(980) production in peripheral pion-nucleon reactions
The Juelich model for pion-pion-scattering, based on an effective meson-meson
Lagrangian is applied to the analysis of the S-wave production amplitudes
derived from the BNL E852 experiment pi^- p -> pi^0 pi^0 n for a pion momentum
of 18.3 GeV. The unexpected strong dependence of the S-wave partial wave
amplitude on the momentum transfer between the proton and neutron in the
vicinity of the f_0(980) resonance is explained in our analysis as interference
effect between the correlated and uncorrelated pi^0 pi^0 pairs.Comment: 6 pages, 7 figures, formulas added, typos removed, new figure
Morita Equivalence, Picard Groupoids and Noncommutative Field Theories
In this article we review recent developments on Morita equivalence of star
products and their Picard groups. We point out the relations between
noncommutative field theories and deformed vector bundles which give the Morita
equivalence bimodules.Comment: Latex2e, 10 pages. Conference Proceeding for the Sendai Meeting 2002.
Some typos fixe
Superfluid pairing in a polarized dipolar Fermi gas
We calculate the critical temperature of a superfluid phase transition in a
polarized Fermi gas of dipolar particles. In this case the order parameter is
anisotropic and has a nontrivial energy dependence. Cooper pairs do not have a
definite value of the angular momentum and are coherent superpositions of all
odd angular momenta. Our results describe prospects for achieving the
superfluid transition in single-component gases of fermionic polar molecules.Comment: 12 pages, 2 figure
Field-linked States of Ultracold Polar Molecules
We explore the character of a novel set of ``field-linked'' states that were
predicted in [A. V. Avdeenkov and J. L. Bohn, Phys. Rev. Lett. 90, 043006
(2003)]. These states exist at ultralow temperatures in the presence of an
electrostatic field, and their properties are strongly dependent on the field's
strength. We clarify the nature of these quasi-bound states by constructing
their wave functions and determining their approximate quantum numbers. As the
properties of field-linked states are strongly defined by anisotropic dipolar
and Stark interactions, we construct adiabatic surfaces as functions of both
the intermolecular distance and the angle that the intermolecular axis makes
with the electric field. Within an adiabatic approximation we solve the 2-D
Schrodinger equation to find bound states, whose energies correlate well with
resonance features found in fully-converged multichannel scattering
calculations
Hydrodynamic excitations of trapped dipolar fermions
A single-component Fermi gas of polarized dipolar particles in a harmonic
trap can undergo a mechanical collapse due to the attractive part of the
dipole-dipole interaction. This phenomenon can be conveniently manipulated by
the shape of the external trapping potential. We investigate the signatures of
the instability by studying the spectrum of low-lying collective excitations of
the system in the hydrodynamic regime. To this end, we employ a time-dependent
variational method as well as exact numerical solutions of the hydrodynamic
equations of the system.Comment: 4 pages, 2 eps figures, final versio
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