1,225 research outputs found
A symmetry reduction technique for higher order Painlev\'e systems
The symmetry reduction of higher order Painlev\'e systems is formulated in
terms of Dirac procedure.
A set of canonical variables that admit Dirac reduction procedure is proposed
for Hamiltonian structures governing the and
Painlev\'e systems for .Comment: to appear in Phys. Lett.
Macdonald's symmetric polynomials as zonal spherical functions on some quantum homogeneous spaces
Quantum analogues of the homogeneous spaces \GL(n)/\SO(n) and
\GL(2n)/\Sp(2n) are introduced. The zonal spherical functions on these
quantum homogeneous spaces are represented by Macdonald's symmetric polynomials
P_{\ld}=P_{\ld}(x_1,\cdots,x_n;q,t) with or
Higgs Mechanism in Nonlocal Field Theories
We study spontaneous gauge symmetry breaking and the Higgs mechanism in
nonlocal field theories. Motivated by the level truncated action of string
field theory, we consider a class of nonlocal field theories with an
exponential factor of the d'Alembertian attached to the kinetic and mass terms.
Modifications of this kind are known to make mild the UV behavior of loop
diagrams and thus have been studied not only in the context of string theory
but also as an alternative approach to quantum gravity. In this paper we argue
that such a nonlocal theory potentially includes a ghost mode near the nonlocal
scale in the particle spectrum of the symmetry broken phase. This is in sharp
contrast to local field theories and would be an obstruction to making a simple
nonlocal model a UV complete theory. We then discuss a possible way out by
studying nonlocal theories with extra symmetries such as gauge symmetries in
higher spacetime dimensions.Comment: 19 pages, 4 figures; v2: references added, version published in JHE
Birational Weyl group action arising from a nilpotent Poisson algebra
We propose a general method to realize an arbitrary Weyl group of Kac-Moody
type as a group of birational canonical transformations, by means of a
nilpotent Poisson algebra. We also give a Lie theoretic interpretation of this
realization in terms of Kac-Moody Lie algebras and Kac-Moody groups.Comment: 31 pages, LaTe
Symmetries in the fourth Painleve equation and Okamoto polynomials
We propose a new representation of the fourth Painlev\'e equation in which
the -symmetries become clearly visible. By means of this
representation, we clarify the internal relation between the fourth Painlev\'e
equation and the modified KP hierarchy. We obtain in particular a complete
description of the rational solutions of the fourth Painlev\'e equation in
terms of Schur functions. This implies that the so-called Okamoto polynomials,
which arise from the -functions for rational solutions, are in fact
expressible by the 3-reduced Schur functions.Comment: 25 pages, amslate
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