Jimbo / Miwa / Tsuchiya Integrable Systems in Quantum Field Theory and Statistical Mechanics

1. Auflage 2014
ISBN: 978-1-4832-9525-1
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 682 Seiten, Web PDF

Integrable Sys Quantum Field Theory

Autoren/Hrsg.

Jimbo, M.

Miwa, T.

Tsuchiya, A.

Inhaltsverzeichnis

1;Front Cover;1
2;Integrable Systems in Quantum Field Theory and Statistical Mechanics;4
3;Copyright Page;5
4;Table of Contents;12
5;Foreword;8
6;Preface to the Present Volume;10
7;Chapter 1. Eigenvalue Spectrum of the Superintegrable Chiral Potts Model;14
7.1;1. Introduction;14
7.2;2. Formalism and the phase I ground state energy;21
7.3;3. Single particle excitation in phases I and IV;36
7.4;4. Multiparticle excitations for Q = 0;40
7.5;5. Discussion;50
7.6;Acknowledgement;53
7.7;Appendix A;54
7.8;Appendix B;57
7.9;Appendix C;59
7.10;References;67
8;Chapter 2. Onsager's Star-Triangle Equation: Master Key to Integrability;70
8.1;1. Introduction;70
8.2;2. Star-triangle equation;71
8.3;3. Chiral Potts model;79
8.4;4. Integrable quantum spin chain;91
8.5;Acknowledgements;96
8.6;Appendix;96
8.7;References;101
9;Chapter 3. Solving Models in Statistical Mechanics;108
9.1;Star-triangle relation;110
9.2;Difference property;112
9.3;Calculation of the free energy;112
9.4;Superintegrable chiral Potts model;123
9.5;References;127
10;Chapter 4. KdV-Type Equations and W-Algebras;130
11;Chapter 5. Boundary Conditions in Conformal Field Theory;140
11.1;1. Introduction;140
11.2;2. Boundary operators in conformal field theory;145
11.3;3. Conformal field theory on an annulus;148
11.4;4. Examples;153
11.5;5. Relation to the corner transfer matrix;155
11.6;6. Virasoro algebra in the non-critical Ising model;157
11.7;Acknowledgements;160
11.8;References;161
12;Chapter 6. Paths, Maya Diagrams and representations of s l ( r, C);162
12.1;1. Introduction;162
12.2;2. Examples;165
12.3;3. The Fock representation of gl(8, C ) , gI(r, C) and sl(r, C);173
12.4;4. Maya diagrams and Plücker relations;180
12.5;5. Paths and lifts;188
12.6;6. Paths and divisors;194
12.7;References;203
13;Chapter 7. Knot Theory based on Solvable Models at Criticality;206
13.1;1. Introduction;207
13.2;2. Yang-Baxter relation;210
13.3;3. Exactly solvable models;221
13.4;4. Knot theory;231
13.5;5. Exactly solvable models and knot theory;242
13.6;6. New link polynomials;258
13.7;7. Two-Variable Extension;274
13.8;8. Related Topics;284
13.9;9. Concluding Remarks;293
13.10;Acknowledgements;294
13.11;References;294
14;Chapter 8. From the Harmonic Oscillator to the A-D-E Classification of Conformal Models;300
14.1;1. Introduction;300
14.2;2. The harmonic oscillator;300
14.3;3. Free particle in a box;305
14.4;4. Rational billiards;311
14.5;5. The A-D-E classification of conformal models;320
14.6;6. Extensions;347
14.7;References;358
15;Chapter 9. Formal Groups and Conformal Field Theory over Z;360
15.1;0. Introduction;360
15.2;1. Formal groups;361
15.3;2. Construction of a formal group;365
15.4;3. Jacobian varieties and t-functions;366
15.5;4. Operators Fn and Vn;371
15.6;5. Zeta functions;375
15.7;References;378
16;Chapter 10. A New Family of Solvable Lattice Models Associated with An(1);380
16.1;1. Introduction;380
16.2;2. Unrestricted models;390
16.3;3. Restricted models;393
16.4;4. Local state probabilities;394
16.5;Appendix A. Proof of Theorem 3;404
16.6;Appendix B. Proof of Theorem 4;406
16.7;Acknowledgements;409
17;Chapter 11. Solvable Lattice Models and Algebras of Face Operators;412
17.1;1. Introduction;412
17.2;2. Solvable lattice models;413
17.3;3. An algebra of face operators;418
17.4;4. An algebra of Yang-Baxter operators;420
17.5;5. Brauer's centralizer algebra and its q-analogue;422
17.6;6. Problems;426
17.7;References;427
18;Chapter 12. D-Modules and Nonlinear Systems;430
18.1;1. Tschirnhaus transformations for algebraic systems;430
18.2;2. Non-linear equations as non-commutative algebras;435
18.3;3 . Linearization;443
18.4;4. Microlocalization;444
19;Chapter 13. Quantum Groups and Integrable Models;448
19.1;1. History of the subject;448
19.2;2. Quantum matrix algebras;453
19.3;3. Quantum groups SLq(n) and GLq(n);456
19.4;4. Quantum groups SOq(n) and Spq(n);459
19.5;5. Quantum simple Lie algebras;463
19.6;6. Problems;467
19.7;References;468
20;Chapter 14. Conformal Field Theory on Universal Family of Stable Curves with Gauge Symmetries;472
20.1;Introduction;472
20.2;Notations;476
20.3;1. Integrable highest weight representation of affine Lie algebra;478
20.4;2. Pointed stable curves and the associated vacua;485
20.5;3. Universal family of pointed stable curves;511
20.6;4. Sheaf of vacua attached to local universal family;533
20.7;5. Integrable Connection with Regular Singularity;542
20.8;6. Locally freeness and factorization;556
20.9;Acknowledgments;576
20.10;References;576
21;Chapter 15. Yang-Baxter Algebras, Conformal Invariant Models and Quantum Groups;580
21.1;1. Yang-Baxter algebras;580
21.2;2. Physical realizations of Yang-Baxter algebras;592
21.3;3. The six vertex model and its descendants;600
21.4;4. Finite-size correctios from the Bethe-ansatz and conformal invariance;613
21.5;5. The light-cone lattice approach;627
21.6;6. Braid groups and quantum groups from Yang-Baxter algebras;644
21.7;References;649
22;Chapter 16. Integrable Field Theory from Conformal Field Theory;654
22.1;1. Introduction;654
22.2;2. Integrals of motion in CFT;658
22.3;3. Equations of motion in perturbed field theory;661
22.4;4. Degenerate fields and integrals of motion;667
22.5;5. Integrals of motion and scattering theory;673
22.6;6. Integrals of motion and S-matrix in critical Ising model with magnetic field;680
22.7;Acknowledgements;685
22.8;References;686
23;Chapter 17. Errata to Vertex Operators in Conformal Field Theory on P1 and Monodromy Representations of Braid Group in Advanced Studies in Pure Mathematics 16,1988;688
23.1;References;695