Conformal field theory and topology / Toshitake Kohno ; [translated from the Japanese by the author].

Format:

Book

Author/Creator:

Kohno, Toshitake.

Series:

Translations of mathematical monographs 0065-9282 ; v. 210.

Iwanami series in modern mathematics

Translations of mathematical monographs, 0065-9282 ; v. 210

Standardized Title:

Ba no riron to toporojī. English

Language:

English

Japanese

Subjects (All):

Conformal invariants.

Quantum field theory.

Topology.

Physical Description:

x, 172 pages : illustrations ; 22 cm.

Place of Publication:

Providence, R.I. : American Mathematical Society, [2002]

Contents:

Chapter 1. Geometric Aspects of Conformal Field Theory 13

1.1. Loop groups and affine Lie algebras 14

1.2. Representations of affine Lie algebras 23

1.3. Wess-Zumino-Witten model 29

1.4. The space of conformal blocks and fusion rules 42

1.5. KZ equation 52

1.6. Vertex operators and OPE 60

Chapter 2. Jones-Witten Theory 75

2.1. KZ equation and representations of braid groups 75

2.2. Conformal field theory and the Jones polynomial 90

2.3. Witten's invariants for 3-manifolds 103

2.4. Projective representations of mapping class groups 110

2.5. Chern-Simons theory and connections on surfaces 121

Chapter 3. Chern-Simons Perturbation Theory 127

3.1. Vassiliev invariants and the Kontsevich integral 127

3.2. Chern-Simons functionals and the Ray-Singer torsion 142

3.3. Chern-Simons perturbative invariants 148

Further Developments and Prospects 157.

Notes:

Includes bibliographical references (pages 165-167) and index.

ISBN:

082182130X

OCLC:

48851341