acta physica slovaca

Acta Physica Slovaca 58, No.6, 811-946 (2008) (135 pages)

Introduction to integrable many-body systems I

Ladislav Ĺ amaj
    Institute of Physics, Slovak Academy of Sciences, 845 11 Bratislava, Slovakia

Full text: ::pdf :: (Received 24 November 2008, accepted 27 November 2008)

Abstract: This is the first volume of a three-volume introductory course about integrable (exactly solvable) systems of interacting bodies. The aim of the course is to derive and analyze, on an elementary mathematical and physical level, the Bethe ansatz solutions, ground-state properties and the thermodynamics of integrable many-body systems in many domains of physics: Nonrelativistic one-dimensional continuum Fermi and Bose gases; One-dimensional quantum models of condensed matter physics like the Heisenberg, Hubbard and Kondo models; Relativistic models of the (1+1)-dimensional Quantum Field Theory like the Luttinger model, the sine-Gordon model and its fermionic analog the Thirring model; Two-dimensional classical models, especially the symmetric Coulomb gas. In the first part of this volume, we deal with nonrelativistic one-dimensional continuum Fermi and Bose quantum gases of spinless (identical) particles with specific types of pairwise interactions like the short-range -function and hard-core interactions, and the long-range 1/x2 interaction. The second part is devoted to the description of the Quantum Inverse Scattering Method, as the universal method for generating and solving integrable models, and to the analysis of the related Yang-Baxter equation, as the consistency condition for the factorization of the multi-particle scattering. With the aid of this method, we present the complete solution of spin-1/2 fermions with δ-function interactions.

PACS: 02.30.Ik, 05.30.Fk, 05.30.Jp, 05.50.+q, 75.10.Jm
Keywords: Integrable systems, Bethe ansatz, Thermodynamics, Scattering matrix, Yang-Baxter equation, Quantum groups
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