930 research outputs found
A -anaolg of the sixth Painlev\'e equation
A -difference analog of the sixth Painlev\'e equation is presented. It
arises as the condition for preserving the connection matrix of linear
-difference equations, in close analogy with the monodromy preserving
deformation of linear differential equations. The continuous limit and special
solutions in terms of -hypergeometric functions are also discussed.Comment: 8 pages, LaTeX file (Two misprints corrected
Isomonodromic deformation with an irregular singularity and the Theta function
We will study a monodromy preserving deformation with an irregular singular
point and determine the function of the monodromy preserving deformation
by the elliptic function moving the argument and the period
.Comment: 30 page
Toda Lattice Hierarchy and Zamolodchikov's Conjecture
In this letter, we show that certain Fredholm determinant ,
introduced by Zamolodchikov in his study of 2D polymers, is a continuum limit
of soliton solution for the Toda lattice hierarchy with 2-periodic reduction
condition.Comment: 6 pages, LaTeX file, no figure
Factorization of R-matrix and Baxter's Q-operator
The general rational solution of the Yang-Baxter equation with the symmetry
algebra sl(2) can be represented as the product of the simpler building blocks
denoted as R-operators. The R-operators are constructed explicitly and have
simple structure. Using the R-operators we construct the two-parametric
Baxter's Q-operator for the generic inhomogeneous periodic XXX spin chain. In
the case of homogeneous XXX spin chain it is possible to reduce the general
Q-operator to the much simpler one-parametric operator.Comment: 17 page
On the Construction of Trigonometric Solutions of the Yang-Baxter Equation
We describe the construction of trigonometric R-matrices corresponding to the
(multiplicity-free) tensor product of any two irreducible representations of a
quantum algebra U_q(\G). Our method is a generalization of the tensor product
graph method to the case of two different representations. It yields the
decomposition of the R-matrix into projection operators. Many new examples of
trigonometric R-matrices (solutions to the spectral parameter dependent
Yang-Baxter equation) are constructed using this approach.Comment: latex file, 29 pages, Universitaet Bielefeld and University of
Queensland preprint, BI-TP-94/13, UQMATH-94-02 (minor correction: in eq.
(4.63) the number 32 should be replaced by 36 and in eq. (4.64) -16 becomes
-18 and -10 becomes -8.
Free Boson Representation of -Vertex Operators and their Correlation Functions
A bosonization scheme of the -vertex operators of \uqa for arbitrary
level is obtained. They act as intertwiners among the highest weight modules
constructed in a bosonic Fock space. An integral formula is proposed for
-point functions and explicit calculation for two-point function is
presented.Comment: 22 pages, latex file, UT-618 (revised version
The BCS theory of q-deformed nucleon pairs - qBCS
We construct a coherent state of q-deformed zero coupled nucleon pairs
distributed in several single-particle orbits. Using a variational approach,
the set of equations of qBCS theory, to be solved self consistently for
occupation probabilities, gap parameter Delta, and the chemical potential
lambda, is obtained. Results for valence nucleons in nuclear degenerate sdg
major shell show that the strongly coupled zero angular momentum nucleon pairs
can be substituted by weakly coupled q-deformed zero angular momentum nucleon
pairs. A study of Sn isotopes reveals a well defined universe of (G, q) values,
for which qBCS converges. While the qBCS and BCS show similar results for Gap
parameter Delta in Sn isotopes, the ground state energies are lower in qBCS.
The pairing correlations in N nucleon system, increase with increasing q (for q
real).Comment: 8 pages, REVTEX, 3 eps figure
An Integrable Model of Quantum Gravity
We present a new quantization scheme for gravity coupled to an
principal chiral field and a dilaton; this model represents a slightly
simplified version of stationary axisymmetric quantum gravity. The analysis
makes use of the separation of variables found in our previous work [1] and is
based on a two-time hamiltonian approach. The quantum constraints are shown to
reduce to a pair of compatible first order equations, with the dilaton playing
the role of a ``clock field''. Exact solutions of the Wheeler-DeWitt equation
are constructed via the integral formula for solutions of the
Knizhnik-Zamolodchiokov equations.Comment: 12 page
Free Boson Realization of
We construct a realization of the quantum affine algebra
of an arbitrary level in terms of free boson fields.
In the limit this realization becomes the Wakimoto
realization of . The screening currents and the vertex
operators(primary fields) are also constructed; the former commutes with
modulo total difference, and the latter creates the
highest weight state from the vacuum state of the boson
Fock space.Comment: 24 pages, LaTeX, RIMS-924, YITP/K-101
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