Conformal Field Theory

Chapter 10 introduces the notion of conformal transformations and the important topic of the massless quantum field theories associated to the critical points of the statistical models. The chapter establishes the important conceptual result that the classification of all possible critical phenomena in two dimensions consists of finding out all possible irreducible representations of the Virasoro algebra. It covers the algebra of local fields, conformal invariance, Polyakov's theorem, quasi-primary fields, Ward identity, primary fields, the Schwartz derivative, the representation theory, radial quantization, the Hilbert space of conformal states, the use of the Cauchy formula, orthogonality of conformal families and structure constants of descendant fields.