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Low-Dimensional Topology and Quantum Field Theory : NATO A S I SERIES SERIES B, PHYSICS - Hugh Osborn

Low-Dimensional Topology and Quantum Field Theory


By: Hugh Osborn (Editor)


Published: 31st October 1993
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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.

Combinatorial recoupling theory and 3-manifold invariantsp. 1
Quantum field theory and A,B,C,D IRF model invariantsp. 19
On combinatorial three-manifold invariantsp. 31
Schwinger-Dyson equation in three dimensional simplicial quantum gravityp. 51
Observables in the Kontsevich modelp. 73
Matrix models in statistical mechanics and quantum field theory, recent examples and problemsp. 85
Dilogarithms and W-algebrasp. 95
Dilogarithm identities and spectra in conformal field theoryp. 99
Physical states in topological coset modelsp. 109
Finite W symmetry in finite dimensional integrable systemsp. 123
On the "Drinfeld-Sokolov" reduction of the Khizhnik-Zamolodchikov equationp. 131
Noncritical dimensions for critical string theory: life beyond the Calabi-Yau frontierp. 143
[actual symbol not reproducible] algebra in two-dimensional black holesp. 159
Graded Lie derivatives and short distance expansions in two dimensionsp. 169
2D Black holes and 2D gravityp. 177
The structure of finite dimensional affine Hecke algebra quotients and their realization in 2D lattice modelsp. 183
An exact renormalisation in a vertex modelp. 193
New representations of the Temperley-Lieb algebra with applicationsp. 203
Order-disorder quantum symmetry in G-spin modelsp. 213
Quantum groups, quantum spacetime and Dirac equationp. 221
Hamiltonian structure of equations appearing in random matricesp. 231
On the existence of pointlike localized fields in conformally invariant quantum physicsp. 247
The phase space of the Wess-Zumino-Witten modelp. 261
Regularization and renormalization of Chern-Simons theoryp. 269
Ray-Singer torsion, topological field theories and the Riemann zeta function at s = 3p. 279
Monstrous moonshine and the uniqueness of the moonshine modulep. 289
Lie algebras and polynomial solutions of differential equationsp. 297
Torus actions, moment maps, and the symplectic geometry of the moduli space of flat connections on a two-manifoldp. 307
Geometric quantization and Witten's semiclassical manifold invariantsp. 317
Indexp. 323
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780306445781
ISBN-10: 0306445786
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 324
Published: 31st October 1993
Publisher: Springer Science+Business Media
Country of Publication: US
Dimensions (cm): 26.67 x 17.78  x 2.54
Weight (kg): 0.82