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This volume contains Introductory Notes and major reprints on conformal field theory and its applications to 2-dimensional statistical mechanics of critical phenomena. The subject relates to many different areas in contemporary physics and mathematics, including string theory, integrable systems, representations of infinite Lie algebras and automorphic functions. Sample Chapter(s). Section 1: General Principles (4,851 KB). Contents: General Principles: Infinite Conformal Symmetry in Two-dimensional Quantum Field Theory (A A Belavin et al.); Conformal Invariance and Surface Critical Behaviour (J Cardy); Mathematical Background: Contravariant Form for Infinite-dimensional Lie Algebras and Superalgebras (V Kac); Verma Modules over the Virasoro Algebra (B Feigin & D Fuks); Unitary Representations of the Virasoro and Super-Virasoro Algebras (P Goddard et al.); Critical Models and Computation of Correlations: Conformal Algebra and Multipoint Correlation Functions in 2D Statistical Models (Vl Dotsenko & V Fateev); On the Identification of Finite Operator Algebras in Two-dimensional Conformally Invariant Field Theories (P Christe & R Flume); Finite Size Scaling: Conformal Invariance, the Central Charge and Universal Finite Size Amplitudes at Criticality (H BlAte et al.); Universal Term in the Free Energy at a Critical Point and the Conformal Anomaly (I Affleck); Exact Surface and Wedge Exponents for Polymers in Two Dimensions (B Duplantier & H Saleur); Modular Invariance: Modular Invariant Partition Functions in Two Dimensions (A Cappelli et al.); Modular Invariant Partition Functions for Parafermionic Field Theories (D Gepner & Z Qiu); Discrete Symmetries of Conformal Theories (J-B Zuber); Connections With Integrable Systems: Exact Exponents for Infinitely many New Multicritical Points (D Huse); Automorphic Properties of Local Height Probabilities for Integrable Solid-on-solid Models (E Date et al.); Models with c = 1: Correlation Functions on the Critical Lines of the Baxter and Ashkin-Teller Models (L Kadanoff & A Brown); Supersymmetric Critical Phenomena and the Two Dimensional Gaussian Model (D Friedan & S Shenker); Curiosities at c=1 (P Ginsparg); Coulomb Gas Picture: Lattice Derivation of Modular Invariant Partition Functions on the Torus (V Pasquier); Vicinity of the Critical Point: Integrals of Motion in Scaling 3-state Potts Model Field Theory (A Zamolodchikov); Correlation Functions and Higher Topology: The Conformal Field Theory of Orbifolds (L Dixon et al.); Conformal and Current Algebras on a General Riemann Surface (T Eguchi & H Ooguri); and other papers. Readership: Theoretical physicists in particle and statistical physics and mathematicians."

Low-dimensional statistical models are instrumental in improving our understanding of emerging fields, such as quantum computing and cryptography, complex systems, and quantum fluids. This book of lectures by international leaders in the field sets these issues into a larger and more coherent theoretical perspective than is currently available.

ETUDE THEORIQUE DES DIVERS ASPECTS DES PHENOMENES CRITIQUES BIDIMENSIONNELS PAR DES METHODES ESSENTIELLEMENT ANALYTIQUES: TRANSFORMATION EN MODELES DE CHAMP LIBRE, EXPLOITATION DE LA SYMETRIE CONFORME. DETERMINATION DES VALEURS EXACTES D'EXPOSANTS CRITIQUES, ET DES EXPRESSIONS DES FONCTIONS DE PARTITION ET DES FONCTIONS DE CORRELATION. TEST D'UN CERTAIN NOMBRE DE RESULTATS PAR DES CALCULS DE MATRICE DE TRANSFERT OU DES SIMULATIONS DE MONTE CARLO