Low-Dimensional Topology and Quantum Field Theory

✍ Scribed by Louis H. Kauffman (auth.), Hugh Osborn (eds.)

• Publisher: Springer US
• Year: 1993
• Tongue: English
• Leaves: 318
• Series: NATO ASI Series 315
• Edition: 1
• Category: Library

✦ Synopsis

The motivations, goals and general culture of theoretical physics and mathematics are different. Most practitioners of either discipline have no necessity for most of the time to keep abreast of the latest developments in the other. However on occasion newly developed mathematical concepts become relevant in theoretical physics and the less rigorous theoretical physics framework may prove valuable in understanding and suggesting new theorems and approaches in pure mathematics. Such interdis­ ciplinary successes invariably cause much rejoicing, as over a prodigal son returned. In recent years the framework provided by quantum field theory and functional in­ tegrals, developed over half a century in theoretical physics, have proved a fertile soil for developments in low dimensional topology and especially knot theory. Given this background it was particularly pleasing that NATO was able to generously sup­ port an Advanced Research Workshop to be held in Cambridge, England from 6th to 12th September 1992 with the title Low Dimensional Topology and Quantum Field Theory. Although independently organised this overlapped as far as some speak­ ers were concerned with a longer term programme with the same title organised by Professor M Green, Professor E Corrigan and Dr R Lickorish. The contents of this proceedings of the workshop demonstrate the breadth of topics now of interest on the interface between theoretical physics and mathematics as well as the sophistication of the mathematical tools required in current theoretical physics.

✦ Table of Contents

Front Matter....Pages i-viii
Combinatorial Recoupling Theory and 3-Manifold Invariants....Pages 1-17
Quantum Field Theory and A,B,C,D IRF Model Invariants....Pages 19-29
On Combinatorial Three-Manifold Invariants....Pages 31-50
Schwinger-Dyson Equation in Three-Dimensional Simplicial Quantum Gravity....Pages 51-71
Observables in the Kontsevich Model....Pages 73-84
Matrix Models in Statistical Mechanics and Quantum Field Theory, Recent Examples and Problems....Pages 85-93
Dilogarithms and W-Algebras....Pages 95-98
Dilogarithm Identities and Spectra in Conformal Field Theory....Pages 99-108
Physical States in Topological Coset Models....Pages 109-122
Finite W Symmetry in Finite Dimensional Integrable Systems....Pages 123-130
On the “Drinfeld-Sokolov” Reduction of the Knizhnik-Zamolodchikov Equation....Pages 131-141
Noncritical Dimensions for Critical String Theory: Life Beyond the Calabi-Yau Frontier....Pages 143-157
W ∞ Algebra in Two-Dimensional Black Holes....Pages 159-167
Graded Lie Derivatives and Short Distance Expansions in Two Dimensions....Pages 169-176
2D Black Holes and 2D Gravity....Pages 177-181
The Structure of Finite Dimensional Affine Hecke Algebra Quotients and their Realization in 2D Lattice Models....Pages 183-191
An Exact Renormalisation in a Vertex Model....Pages 193-201
New Representations of the Temperley-Lieb Algebra with Applications....Pages 203-212
Order-Disorder Quantum Symmetry in G -Spin Models....Pages 213-220
Quantum Groups, Quantum Spacetime, and Dirac Equation....Pages 221-230
Hamiltonian Structure of Equations Appearing in Random Matrices....Pages 231-245
On the Existence of Pointlike Localized Fields in Conformally Invariant Quantum Physics....Pages 247-259
The Phase Space of the Wess-Zumino-Witten Model....Pages 261-267
Regularization and Renormalization of Chern-Simons Theory....Pages 269-278
Ray-Singer Torsion, Topological Field Theories and the Riemann Zeta Function at s = 3....Pages 279-288
Monstrous Moonshine and the Uniqueness of the Moonshine Module....Pages 289-296
Lie Algebras and Polynomial Solutions of Differential Equations....Pages 297-305
Torus Actions, Moment Maps, and the Symplectic Geometry of the Moduli Space of Flat Connections on a Two-Manifold....Pages 307-316
Geometric Quantization and Witten’s Semiclassical Manifold Invariants....Pages 317-322
Back Matter....Pages 323-324

✦ Subjects

Nuclear Physics, Heavy Ions, Hadrons; Theoretical, Mathematical and Computational Physics; Mathematics, general