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Conformal Quantum Field Theory in D-Dimensions

This volume reviews recent developments in conformal quantum field theory in D-dimensions, and focuses on two main aims. Firstly, the promising trend is followed toward constructing an exact solution for a certain class of models. Work on the conformal Ward identities in a D-dimensional space in the late '70s suggests a parallel with the null-vectors which determine the minimal models in the two-dimensional field theory. Recent research has also indicated the possible existence of an infinite parameter algebra analogous to the Virasoro algebra in spaces of higher dimensions D>=3. Each of these models contains parameters similar to the central charge of the two-dimensional theory, due to special fields which occur in the commutator of the components of the energy-momentum tensor. As a first step, a special formalism is suggested which allows finding an exact solution of these models for any space dimension. Then it is shown that in each model closed differential equations can be obtained for higher correlators, as well as the algebraic equations for scale dimensions of fields, and dimensionless parameters similar to the central charge. Secondly, this work aims to give a survey of some special aspects of conformal quantum field theory in D-dimensional space. Included are the survey of conformal methods of approximate calculation of critical indices in a three-dimensional space, an analysis and solution of a renormalised system of Schwinger-Dyson equations, a derivation of partial wave expansions, among other topics. Special attention is given to the development of the apparatus of quantum conform theory of gauge fields. Audience: This book will be of interest to graduate students and researchers whose work involves quantum field theory.
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Table of Contents

Preface. I: Goals and Perspectives. II: Global Conformal Symmetry and Hilbert Space. III: Euclidean Formulation of the Conformal Theory. IV: Approximate Methods of Calculating Critical Indices. VI: Ward Identities. VII: Contribution of Electromagnetic and Gravitational Interactions into the General Solution of Ward Identities. VIII: Dynamical Sector of the Hilbert Space. IX: Conformal Invariance in Gauge Theories. X: Special Features of Conformal Transformation of Current, Energy-Momentum Tensor and Gauge Fields. Appendix I: Casimir Operators and Irreducible Representations of Conformal Group of 4-Dimensional Minkowski Space. Appendix II: Fourier Transforms of Euclidean and Minkowski Spaces Invariant Functions. Appendix III: Calculation of Euclidean Quasilocal Invariant Three-Point Functions. Appendix IV: An Invariance Under Subgroups SO(D-1,2) and SO(D) x SO(2). Appendix V: The Derivation of the Anomalous Ward Identities for Green Functions

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