Integrable Systems in Quantum Field Theory and Statistical Mechanics
Michio Jimbo, T. Miwa, A. Tsuchiya
Advanced Studies in Pure Mathematics, Volume 19: Integrable Systems in Quantum Field Theory and Statistical Mechanics provides information pertinent to the advances in the study of pure mathematics. This book covers a variety of topics, including statistical mechanics, eigenvalue spectrum, conformal field theory, quantum groups and integrable models, integrable field theory, and conformal invariant models. Organized into 17 chapters, this volume begins with an overview of the eigenvalues of the three-state superintegrable chiral Potts model of the associated spin chain by use of a functional equation. This text then illustrates the importance of the star-triangle equation with a few results for the two-dimensional Ising model. Other chapters consider the conformal field theories on manifolds with a boundary, and the constraints placed by modular invariance on their partition functions. This book discusses as well the topological invariants for knots and links. The final chapter deals with equations of motion for two-dimensional quantum field theory. This book is a valuable resource for mathematicians.
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Contents
G ALBERTINI B M McCoy and J H H PERK Eigenvalue Spec
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88 |
149
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259 |
ITZYKSON From the Harmonic Oscillator to the ADE Clas
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287 |
Copyright
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Other editions - View all
Integrable Systems in Quantum Field Theory and Statistical Mechanics M. Jimbo,T. Miwa,A. Tsuchiya Limited preview - 2014 |
Common terms and phrases
affine Lie algebra Baxter Boltzmann weights boundary conditions braid group chiral Potts model coefficients commutative conformal field theory consider construct corresponding D-module defined denote differential dimensional divisor eigenvalues element equation exact sequence factor fermion finite formal genus given Hamiltonian Hence highest weight holomorphic integrable invariant IRF models irreducible Ising model isomorphism Jimbo knot Lemma Lett linear link polynomial mapping Markov property Markov trace Math meromorphic Miwa N-pointed stable curve neighbourhoods notation Nucl obtain pair parameter particles partition function phase Phys Potts model preprint Proof Proposition quantum groups relation representation Reshetikhin resp S-matrix satisfies sheaf sinh six-vertex model solution solvable models spin star-triangle Statistical Mechanics subalgebra symmetry Theorem transfer matrix transformation universal family variables vector space vertex model Virasoro algebra Young diagram Zamolodchikov