Mathphys Odyssey 2001: Integrable Models and Beyond in Honor of Barry M. McCoy

ISBN-13: 9781461266051 / Angielski / Miękka / 2012 / 476 str.

Masaki Kashiwara; Tetsuji Miwa

Opis

This volume is dedicated to Barry M. McCoy on the occasionofhis sixtieth birthday. Barry McCoy has led the research on integrable models in statistical mechanics and quantumfieldtheoryfor morethan 30years. Hisbook, cowrittenwithT.T.Wu, The Two dimensional/sing Model, (HarvardUniversity)containsallthebasic resultsontheIsing model obtained by the early 1970s. However, McCoy'sjointpaper with Wu, Tracy and Barouch, Spin-spin correlation functions for the two-dimensional/sing model: Exact results in the scaling region (Physical Review B13, 316-374, 1976), was a giant step beyond the book. A remarkable connection between the two-point scaling correlation functions and the Painleve transcendents was found. This work made an enormous impact on mathematical physics in the last quarter of the 20th century. It gave the first nontrivial exampleofinteracting field theory in which the Green function can be written explicitly in terms of special functions satisfying nonlinear differential equations. Later in the 1980s, an extensive list of massless field theories was added in the innovation of conformal field theory, in which the Green functions are characterized by linear differential equationsofthe hypergeometric type. However, evenalmost30yearsaftertheirwork, theIsingmodel isessentiallytheunique casewhereall theGreenfunctionsofmassivefield theoryarecharacterizedbynonlinear differential equations."

Spis treści

Preface * Wavevector-Dependent Susceptibilities in Aperiodic Planar Models * Correlation Functions and Susceptibility in the Z-Invariant Ising Model * A Rapidity-independent Parameter in the Star-Triangle Relation * Evaluation of Integrals Representing Correlations in XXX Heisenberg Spin Chain * A Note on Quotients of the Onsager Algebra * Evaluation Parameters and Bethe Roots for the Six Vertex Model at Roots of Unity * Normalization Factors, Reflection Amplitudes and Integrable Systems * Vertex Operator Algebra Arising from the Minimal Series M(3,p) and Monomial Basis * Paths Crystals and Fermionic Formulae * The Nonlinear Steepest Descent Approach to the Asymtpotis of the Second Painlevé Transcendent in the Complex Domain * Generalized Umemura Polynomials and Hirota-Miwa Equation * Correlation Functions of Quantum Integrable Models: The XXZ Spin Chain * On Form Factors of SU(2) Invariant Thirring Model * Integrable Boundaries and Universal TBA Functional Equations * Conformal Field Theories, Graphs and Quantum Algebras * q-Supernomial Coefficients: From Rigging to Ribbons * Separation of Variables for Quantum Integrable Models Related to Uq(slN) * On a Distribution Function Arising in Computational Biology

O autorze

Developments in mathematical physics during the second half of the 20th century influenced a number of mathematical areas, among the more significant being representation theory, differential equations, combinatorics, and algebraic geometry. In all areas, the dynamic role of integrable models has been central. This volume focuses on the ongoing importance of integrability in: conformal field theory, massive quantum field theory, solvable lattice models, quantum affine algebras, the Painlevé equations and combinatorics. Will serve as an excellent reference text for mathematical physicists and graduate students.