Low-Dimensional Topology and Quantum Field Theory / Edition 1

by Hugh Osborn

Overview

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.

Product Details

ISBN-13:	9780306445781
Publisher:	Springer US
Publication date:	10/31/1993
Series:	NATO Science Series B: , #315
Edition description:	1993
Pages:	324
Product dimensions:	7.01(w) x 10.00(h) x 0.03(d)

Table of Contents

Combinatorial recoupling theory and 3-manifold invariants.- Quantum field theory and A,B,C,D IRF model invariants.- On combinatorial three-manifold invariants.- Schwinger-Dyson equation in three dimensional simplicial quantum gravity.- Observables in the Kontsevich model.- Matrix models in statistical mechanics and quantum field theory, recent examples and problems.- Dilogarithms and W-algebras.- Dilogarithm identities and spectra in conformal field theory.- Physical states in topological coset models.- Finite W symmetry in finite dimensional integrable systems.- On the “Drinfeld-Sokolov” reduction of the Khizhnik-Zamolodchikov equation.- Noncritical dimensions for critical string theory: life beyond the Calabi-Yau frontier.- W? algebra in two-dimensional black holes.- Graded Lie derivatives and short distance expansions in two dimensions.- 2D Black holes and 2D gravity.- The structure of finite dimensional affine Hecke algebra quotients and their realization in 2D lattice models.- An exact renormalisation in a vertex model.- New representations of the Temperley-Lieb algebra with applications.- Order-disorder quantum symmetry in G-spin models.- Quantum groups, quantum spacetime and Dirac equation.- Hamiltonian structure of equations appearing in random matrices.- On the existence of pointlike localized fields in conformally invariant quantum physics.- The phase space of the Wess-Zumino-Witten model.- Regularization and renormalization of Chern-Simons theory.- Ray-Singer torsion, topological field theories and the Riemann zeta function at s = 3.- Monstrous moonshine and the uniqueness of the moonshine module.- Lie algebras and polynomial solutions of differential equations.- Torus actions, moment maps, and the symplectic geometry of the moduli space of flatconnections on a two-manifold.- Geometric quantization and Witten’s semiclassical manifold invariants.

Editorial Reviews

Mathematicians and theoretical physicists don't generally speak to each other, because they don't have to. But now and then a discovery is made in one field that can be of use in the other. Some of the interesting topics currently at the interface of the two disciplines are discussed in 29 papers from a workshop in Cambridge, England, September 1992. Among them are observables in the Kontsevich model, physical states in topological coset models, and the existence of pointlike localized fields in conformally invariant quantum physics. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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