1,294 research outputs found
Hamiltonian Dynamics, Classical R-matrices and Isomonodromic Deformations
The Hamiltonian approach to the theory of dual isomonodromic deformations is
developed within the framework of rational classical R-matrix structures on
loop algebras. Particular solutions to the isomonodromic deformation equations
appearing in the computation of correlation functions in integrable quantum
field theory models are constructed through the Riemann-Hilbert problem method.
The corresponding -functions are shown to be given by the Fredholm
determinant of a special class of integral operators.Comment: LaTeX 13pgs (requires lamuphys.sty). Text of talk given at workshop:
Supersymmetric and Integrable Systems, University of Illinois, Chicago
Circle, June 12-14, 1997. To appear in: Springer Lecture notes in Physic
Free field constructions for the elliptic algebra and Baxter's eight-vertex model
Three examples of free field constructions for the vertex operators of the
elliptic quantum group are obtained. Two of these
(for ) are based on representation theories
of the deformed Virasoro algebra, which correspond to the level 4 and level 2
-algebra of Lepowsky and Wilson. The third one () is
constructed over a tensor product of a bosonic and a fermionic Fock spaces. The
algebraic structure at , however, is not related to the deformed
Virasoro algebra. Using these free field constructions, an integral formula for
the correlation functions of Baxter's eight-vertex model is obtained. This
formula shows different structure compared with the one obtained by Lashkevich
and Pugai.Comment: 23 pages. Based on talks given at "MATHPHYS ODYSSEY 2001-Integrable
Models and Beyond" at Okayama and Kyoto, February 19-23, 2001, et
Elliptic algebra U_{q,p}(^sl_2): Drinfeld currents and vertex operators
We investigate the structure of the elliptic algebra U_{q,p}(^sl_2)
introduced earlier by one of the authors. Our construction is based on a new
set of generating series in the quantum affine algebra U_q(^sl_2), which are
elliptic analogs of the Drinfeld currents. They enable us to identify
U_{q,p}(^sl_2) with the tensor product of U_q(^sl_2) and a Heisenberg algebra
generated by P,Q with [Q,P]=1. In terms of these currents, we construct an L
operator satisfying the dynamical RLL relation in the presence of the central
element c. The vertex operators of Lukyanov and Pugai arise as `intertwiners'
of U_{q,p}(^sl_2) for level one representation, in the sense to be elaborated
on in the text. We also present vertex operators with higher level/spin in the
free field representation.Comment: 49 pages, (AMS-)LaTeX ; added an explanation of integration contours;
added comments. To appear in Comm. Math. Phys. Numbering of equations is
correcte
The Analytic Structure of Trigonometric S Matrices
-matrices associated to the vector representations of the quantum groups
for the classical Lie algebras are constructed. For the and
algebras the complete -matrix is found by an application of the bootstrap
equations. It is shown that the simplest form for the -matrix which
generalizes that of the Gross-Neveu model is not consistent for the
non-simply-laced algebras due to the existence of unexplained singularities on
the physical strip. However, a form which generalizes the -matrix of the
principal chiral model is shown to be consistent via an argument which uses a
novel application of the Coleman-Thun mechanism. The analysis also gives a
correct description of the analytic structure of the -matrix of the
principle chiral model for .Comment: 25 pages (macro included, 6 figures included as uuencoded compressed
tar file), CERN-TH.6888/93, (An important argument is corrected leading to a
novel application of the Coleman-Thun mechanism. Also decided to risk some
figures.
Vertex operator approach for correlation functions of Belavin's (Z/nZ)-symmetric model
Belavin's -symmetric model is considered on the
basis of bosonization of vertex operators in the model and
vertex-face transformation. The corner transfer matrix (CTM) Hamiltonian of
-symmetric model and tail operators are expressed in
terms of bosonized vertex operators in the model. Correlation
functions of -symmetric model can be obtained by
using these objects, in principle. In particular, we calculate spontaneous
polarization, which reproduces the result by myselves in 1993.Comment: For the next thirty days the full text of this article is available
at http://stacks.iop.org/1751-8121/42/16521
Fusion of the -Vertex Operators and its Application to Solvable Vertex Models
We diagonalize the transfer matrix of the inhomogeneous vertex models of the
6-vertex type in the anti-ferroelectric regime intoducing new types of q-vertex
operators. The special cases of those models were used to diagonalize the s-d
exchange model\cite{W,A,FW1}. New vertex operators are constructed from the
level one vertex operators by the fusion procedure and have the description by
bosons. In order to clarify the particle structure we estabish new isomorphisms
of crystals. The results are very simple and figure out representation
theoretically the ground state degenerations.Comment: 35 page
Impurity Operators in RSOS Models
We give a construction of impurity operators in the `algebraic analysis'
picture of RSOS models. Physically, these operators are half-infinite
insertions of certain fusion-RSOS Boltzmann weights. They are the face analogue
of insertions of higher spin lines in vertex models. Mathematically, they are
given in terms of intertwiners of modules. We present a
detailed perturbation theory check of the conjectural correspondence between
the physical and mathematical constructions in a particular simple example.Comment: Latex, 24 pages, uses amsmath, amsthm, amssymb, epic, eepic and
texdraw style files (Minor typos corrected) (minor changes
Quantum groups and q-lattices in phase space
Quantum groups lead to an algebraic structure that can be realized on quantum
spaces. These are noncommutative spaces that inherit a well defined
mathematical structure from the quantum group symmetry. In turn such quantum
spaces can be interpreted as noncommutative configuration spaces for physical
systems which carry a symmetry like structure. These configuration spaces will
be generalized to noncommutative phase space. The definition of the
noncommutative phase space will be based on a differential calculus on the
configuration space which is compatible with the symmetry. In addition a
conjugation operation will be defined which will allow us to define the phase
space variables in terms of algebraically selfadjoint operators. An interesting
property of the phase space observables will be that they will have a discrete
spectrum. These noncommutative phase space puts physics on a lattice structure.Comment: 6 pages, Postscrip
Free Field Approach to the Dilute A_L Models
We construct a free field realization of vertex operators of the dilute A_L
models along with the Felder complex. For L=3, we also study an E_8 structure
in terms of the deformed Virasoro currents.Comment: (AMS-)LaTeX(2e), 43page
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