Searcharxiv⌕ Search

arXiv subjects

I. G. Korepanov

Publications and source records attributed to I. G. Korepanov.

30 records · Page 2Linked to original sources
arXiv1998

Eigenvector and eigenvalue problem for 3D bosonic model

In this paper we reformulate free field theory models defined on the rectangular $D+1$ dimensional lattices as $D+1$ evolution models. This evolution is in part a simple linear evolution on free (``creation'' and ``annihilation'') operators. Formal eigenvectors of this linear evolution can be directly constructed, and them play the role of the ``physical'' creation and annihilation operators. These operators being completed by a ``physical'' vacuum vector give the spectrum of the evolution operator, as well as the trace of the evolution operator give a correct expression for the partition function. As an example, Bazhanov -- Baxter's free bosonic model is considered.

solv-int↗
arXiv1998

Functional Tetrahedron Equation

We describe a scheme of constructing classical integrable models in 2+1-dimensional discrete space-time, based on the functional tetrahedron equation - equation that makes manifest the symmetries of a model in local form. We construct a very general "block-matrix model" together with its algebro-geometric solutions, study its various particular cases, and also present a remarkably simple scheme of quantization for one of those cases.

solv-int↗
arXiv1997

Some eigenstates for a model associated with solutions of tetrahedron equation. V. Two cases of string superposition

In paper IV (solv-int/9704013) we have considered a string living in the infinite lattice that was, in a sense, generated by a "particle". Here we show how to construct multi-string eigenstates generated by several particles. It turns out that, at least in some cases, this allows us to bypass the difficulties of constructing multi-particle states. We also present and discuss the "dispersion relations" for our particles-strings.

solv-int↗
arXiv1997

Some eigenstates for a model associated with solutions of tetrahedron equation. II. A bit of algebraization

This paper adds two observations to the work solv-int/9701016 where some eigenstates for a model based on tetrahedron equation have been constructed. The first observation is that there exists a more "algebraic" construction of one-particle states, resembling the 1+1-dimensional algebraic Bethe ansatz. The second observation is that the strings introduced in solv-int/9701016 are symmetries of a transfer matrix, rather than just eigenstates.

solv-int↗
arXiv1997

Some eigenstates for a model associated with solutions of tetrahedron equation

Here we present some eigenstates for a 2+1-dimensional model associated with a solution of the tetrahedron equation. The eigenstates include those "particle-like" (namely one-particle and two-particle ones), constructed in analogy with the usual 1+1-dimensional Bethe ansatz, and some simple "string-like" ones.

solv-int↗
arXiv1995

Algebraic integrable dynamical systems, 2+1-dimensional models in wholly discrete space-time, and inhomogeneous models in 2-dimensional statistical physics

This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in 2+1-dimensional wholly discrete space-time, and to connection between those field theories and inhomogoneous models in 2-dimensional statistical physics.

solv-int↗
arXiv1994

A Dynamical System Connected with Inhomogeneous 6-Vertex Model

A completely integrable dynamical system in discrete time is studied by means of algebraic geometry. The system is associated with factorization of a linear operator acting in a direct sum of three linear spaces into a product of three operators, each acting nontrivially only in a direct sum of two spaces, and the following reversing of the order of factors. There exists a reduction of the system interpreted as a classical field theory in 2+1-dimensional space-time, the integrals of motion coinciding, in essence, with the statistical sum of an inhomogeneous 6-vertex free-fermion model on the 2-dimensional kagome lattice (here the statistical sum is a function of two parameters). Thus, a connection with the ``local'', or ``generalized'', quantum Yang--Baxter equation is revealed.

hep-th↗
arXiv1994

Tetrahedron equation and the algebraic geometry

The tetrahedron equation arises as a generalization of the famous Yang--Baxter equation to the 2+1-dimensional quantum field theory and the 3-dimensional statistical mechanics. Very little is still known about its solutions. Here a systematic method is described that does produce non-trivial solutions to the tetrahedron equation with spin-like variables on the links. The essence of the method is the use of the so-called tetrahedral Zamolodchikov algebras.

hep-th↗
arXiv1993

Vacuum curves, classical integrable systems in discrete space-time and statistical physics

A dynamical system with discrete time is studied by means of algebraic geometry. The system admits a reduction that is interpreted as a classical field theory in 2+1-dimensional wholly discrete space-time. The integrals of motion of a particular case of the reduced system are shown to coincide, in essence, with the statistical sum of the well-known (inhomogeneous) 2-dimensional dimer model (the statistical sum is here a function of two parameters). Possible generalizations of the system are examined.

hep-th↗