Infinite conformal symmetry in two-dimensional quantum field theory by BPZ

The basic idea of the foundational work on conformal field theory is to use degenerate representations of to write down differential equations for correlation functions

Their results were first applied to two-dimensional critical behaviour in a ground-breaking paper by their compatriots Alexander Belavin, Alexander Polyakov and Alexander Zamolodchikov (BPZ) in 1984. They showed the existence of a whole set of conformal field theories,called the minimal models, where only a finite set of representations, all of the degenerate type, occur. In these models, then, the reduction of the vastly complex problem of an interacting, scale-invariant, field theory to a finite one, mentioned in the introduction, is realised. It then turns out that these models may be solved completely, in the sense that all possible correlation functions (including those depending on more than two points) are exactly calculable. The correlation functions satisfy differential equations which are simple generalisations of the hypergeometric equation, and their solutions may be represented in terms of contour integrals. Nearly all of the standard functions of 19th century mathematical physics (Bessel functions, Legendre polynomials, etc) may be thought of as special cases of the hypergeometric function, so its appearance in this context is particularly fascinating. The somewhat technical assumption of BPZ that only degenerate representations occur was quickly clarified by Daniel Friedan, Zongan Qiu and Stephen Shenker in the US, who showed that, for c< 1 at least, the only acceptable conformal field theories are minimal models. What came out of this analysis was a remarkable formula, named after Kac, for the allowed values of the scaling dimensions for most types of two-dimensional critical behaviour:

articles

• Infinite conformal symmetry in two-dimensional quantum field theory
  • Alexander Belavin, Alexander Polyakov and Alexander Zamolodchikov, Nucl. Phys. B241 (1984) 333–380

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• ID : Q29542407

Spacy 패턴 목록

• [{'LOWER': 'infinite'}, {'LOWER': 'conformal'}, {'LOWER': 'symmetry'}, {'LOWER': 'in'}, {'LOWER': 'two'}, {'OP': '*'}, {'LOWER': 'dimensional'}, {'LOWER': 'quantum'}, {'LOWER': 'field'}, {'LEMMA': 'theory'}]