This book reviews recent developments of the conformally invariant field theory in D dimensions. Exactly solvable models, conformal gauge theories, the methods of approximate calculations of the critical indices in the phase transition theory and spontaneous breaking of conformal symmetry are considered. The main focus is on solvable models in D dimensions. Operator products, renormalized Schwinger-Dyson equations, and conformal Ward identities are analyzed for this purpose. A class of solvable models is found and the method for solving them is formulated. The scalar field with the scale dimension D-2 appears in each of these models as a consequence of self-consistency. This scalar field in D dimensions is an operator analogue to the central charge in two dimension space.
Publisher: World Scientific Publishing Co Pte Ltd
Number of pages: 300
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