278 research outputs found
Integrable Generalized Principal Chiral Models
We study 2D non-linear sigma models on a group manifold with a special form
of the metric. We address the question of integrability for this special class
of sigma models. We derive two algebraic conditions for the metric on the group
manifold. Each solution of these conditions defines an integrable model.
Although the algebraic system is overdetermined in general, we give two
examples of solutions. We find the Lax field for these models and calculate
their Poisson brackets. We also obtain the renormalization group (RG)
equations, to first order, for the generic model. We solve the RG equations for
the examples we have and show that they are integrable along the RG flow.Comment: 14 pages, harvmac (l
Flat Connections for Characters in Irrational Conformal Field Theory
Following the paradigm on the sphere, we begin the study of irrational
conformal field theory (ICFT) on the torus. In particular, we find that the
affine-Virasoro characters of ICFT satisfy heat-like differential equations
with flat connections. As a first example, we solve the system for the general
coset construction, obtaining an integral representation for the general
coset characters. In a second application, we solve for the high-level
characters of the general ICFT on simple , noting a simplification for the
subspace of theories which possess a non-trivial symmetry group. Finally, we
give a geometric formulation of the system in which the flat connections are
generalized Laplacians on the centrally-extended loop group.Comment: harvmac (answer b to question) 40 pages. LBL-35718, UCB-PTH-94/1
The finite harmonic oscillator and its associated sequences
A system of functions (signals) on the finite line, called the oscillator
system, is described and studied. Applications of this system for discrete
radar and digital communication theory are explained.
Keywords: Weil representation, commutative subgroups, eigenfunctions, random
behavior, deterministic constructionComment: Published in the Proceedings of the National Academy of Sciences of
the United States of America (Communicated by Joseph Bernstein, Tel Aviv
University, Tel Aviv, Israel
Principal models on a solvable group with nonconstant metric
Field equations for generalized principle models with nonconstant metric are
derived and ansatz for their Lax pairs is given. Equations that define the Lax
pairs are solved for the simplest solvable group. The solution is dependent on
one free variable that can serve as the spectral parameter. Painleve analysis
of the resulting model is performed and its particular solutions are foundComment: 8 pages, Latex2e, no figure
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