Astérisque 2013; 136 pp; softcover Number: 353 ISBN13: 9782856293690 List Price: US$52 Member Price: US$41.60 Order Code: AST/353
 In these mostly expository lectures, the authors give an elementary introduction to conformal field theory in the context of probability theory and complex analysis. The authors consider statistical fields and define Ward functionals in terms of their Lie derivatives. Based on this approach, the authors explain some equations of conformal field theory and outline their relation to SLE theory. A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list. Readership Graduate students and research mathematicians interested in conformal field theory and SchrammLoewner Evolution. Table of Contents  Introduction
 Lecture 1. Fock space fields
 Appendix 2. Fock space fields as (very) generalized random functions
 Lecture 3. Operator product expansion
 Lecture 4. Conformal geometry of Fock space fields
 Lecture 5. Stress tensor and Ward's identities
 Appendix 6. Ward's identities for finite BoltzmannGibbs ensembles
 Lecture 7. Virasoro field and representation theory
 Appendix 8. Existence of the Virasoro field
 Appendix 9. Operator algebra formalism
 Lecture 10. Modications of the Gaussian free field
 Appendix 11. Current primary fields and KZ equations
 Lecture 12. Multivalued conformal Fock space fields
 Appendix 13. CFT and SLE numerology
 Lecture 14. Connection to SLE theory
 Lecture 15. Vertex observables
 Bibliography
 Index
