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Petr P. Kulish

Bio: Petr P. Kulish is an academic researcher from Steklov Mathematical Institute. The author has contributed to research in topics: Quantum group & Yang–Baxter equation. The author has an hindex of 24, co-authored 103 publications receiving 6295 citations. Previous affiliations of Petr P. Kulish include St. Petersburg Department of Steklov Institute of Mathematics & University of the Algarve.


Papers
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Journal ArticleDOI
TL;DR: In this article, the problem of constructing the GL(N,ℂ) solutions to the Yang-Baxter equation (factorizedS-matrices) is considered.
Abstract: The problem of constructing the GL(N,ℂ) solutions to the Yang-Baxter equation (factorizedS-matrices) is considered. In caseN=2 all the solutions for arbitrarily finite-dimensional irreducible representations of GL(2,ℂ) are obtained and their eigenvalues are calculated. Some results for the caseN>2 are also presented.

979 citations

Journal ArticleDOI
TL;DR: By invoking the twisted Poincare symmetry of the algebra of functions on a Minkowski space-time, this paper showed that the non-commutative space time with the commutation relations [ x μ, x ν ] = i θ μ ν, where θμ ν is a constant real antisymmetric matrix, can be interpreted in a Lorentz-invariant way.

655 citations

Journal ArticleDOI
TL;DR: In this paper, a quantum linear problem is constructed which permits the investigation of the sine-Gordon equation within the framework of the inverse scattering method in an arbitrary representation of algebra and geometry.
Abstract: A quantum linear problem is constructed which permits the investigation of the sine-Gordon equation within the framework of the inverse scattering method in an arbitrary representation of algebra . The corresponding R-matrix is found, satisfying the Yang-Baxter equation (the condition for the factorization of the multiparticle matrices of the scattering of particles on a straight line).

537 citations

Journal ArticleDOI
TL;DR: In this paper, the authors give the basic definitions connected with the Yang-Baxter equation (factorization condition for a multiparticle S-matrix) and formulate the problem of classifying its solutions.
Abstract: We give the basic definitions connected with the Yang-Baxter equation (factorization condition for a multiparticle S-matrix) and formulate the problem of classifying its solutions. We list the known methods of solution of the Y-B equation, and also various applications of this equation to the theory of completely integrable quantum and classical systems. A generalization of the Y-B equation to the case ofZ 2-graduation is obtained, a possible connection with the theory of representations is noted. The supplement contains about 20 explicit solutions.

468 citations


Cited by
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Journal ArticleDOI
01 Dec 1949-Nature
TL;DR: Wentzel and Jauch as discussed by the authors described the symmetrization of the energy momentum tensor according to the Belinfante Quantum Theory of Fields (BQF).
Abstract: To say that this is the best book on the quantum theory of fields is no praise, since to my knowledge it is the only book on this subject But it is a very good and most useful book The original was written in German and appeared in 1942 This is a translation with some minor changes A few remarks have been added, concerning meson theory and nuclear forces, also footnotes referring to modern work in this field, and finally an appendix on the symmetrization of the energy momentum tensor according to Belinfante Quantum Theory of Fields Prof Gregor Wentzel Translated from the German by Charlotte Houtermans and J M Jauch Pp ix + 224, (New York and London: Interscience Publishers, Inc, 1949) 36s

2,935 citations

Journal ArticleDOI
TL;DR: Aq-difference analogue of the universal enveloping algebra U(g) of a simple Lie algebra g is introduced in this article, and its structure and representations are studied in the simplest case g=sl(2).
Abstract: Aq-difference analogue of the universal enveloping algebra U(g) of a simple Lie algebra g is introduced. Its structure and representations are studied in the simplest case g=sl(2). It is then applied to determine the eigenvalues of the trigonometric solution of the Yang-Baxter equation related to sl(2) in an arbitrary finite-dimensional irreducible representation.

2,767 citations

20 Jul 1986

2,037 citations

Journal ArticleDOI
TL;DR: Baxter has inherited the mantle of Onsager who started the process by solving exactly the two-dimensional Ising model in 1944 as mentioned in this paper, and there has been a growing belief that all the twodimensional lattice statistical models will eventually be solved and that it will be Professor Baxter who solves them.
Abstract: R J Baxter 1982 London: Academic xii + 486 pp price £43.60 Over the past few years there has been a growing belief that all the twodimensional lattice statistical models will eventually be solved and that it will be Professor Baxter who solves them. Baxter has inherited the mantle of Onsager who started the process by solving exactly the two-dimensional Ising model in 1944.

1,658 citations

Book ChapterDOI
24 Sep 1987
TL;DR: The quantum inverse scattering method for solving nonlinear equations of evolution, the quantum theory of magnets, the method of commuting transfer-matrices in classical statistical mechanics, and factorizable scattering theory as discussed by the authors emerged as a natural development of the various directions in mathematical physics.
Abstract: Publisher Summary This chapter focuses on the quantization of lie groups and lie algebras. The Algebraic Bethe Ansatz—the quantum inverse scattering method—emerges as a natural development of the various directions in mathematical physics: the inverse scattering method for solving nonlinear equations of evolution, the quantum theory of magnets, the method of commuting transfer-matrices in classical statistical mechanics, and factorizable scattering theory. The chapter discusses quantum formal groups, a finite-dimensional example, an infinite-dimensional example, and reviews the deformation theory and quantum groups.

1,584 citations