This work provides a systematic introduction to quantum field theory and renormalization group, as applied to particle physics and continuous macroscopic phase transitions.
This work provides a systematic introduction to quantum field theory and renormalization group, as applied to particle physics and continuous macroscopic phase transitions.
Jean Zinn-Justin, Scientific Advisor, CEA, Paris-Saclay. Jean Zinn-Justin has worked as a theoretical and mathematical physicist at Saclay Nuclear Research Centre (CEA) since 1965, where he was also Head of the Institute of Theoretical Physics from 1993-1998. Since 2010 he has also held the position of Adjunct Professor at Shanghai University. Previously he has served as a visiting professor at the Massachusetts Institute of Technology (MIT), Princeton University, State University of New York at Stony Brook, and Harvard University. He directed the Les Houches Summer School for theoretical physics from 1987 to 1995. He has served on editorial boards for several influential physics journals including the French Journal de Physique, Nuclear Physics B, Journal of Physics A, and the New Journal of Physics.
Inhaltsangabe
* Preface * 1: Gaussian integrals. Algebraic preliminaries * 2: Euclidean path integrals and quantum mechanics * 3: Quantum mechanics: Path integrals in phase space * 4: Quantum statistical physics: Functional integration formalism * 5: Quantum evolution: From particles to fields * 6: The neutral relativistic scalar field * 7: Perturbative quantum field theory: Algebraic methods * 8: Ultraviolet divergences: Effective quantum field theory * 9: Introduction to renormalization theory and renormalization group * 10: Dimensional continuation, regularization. Minimal subtraction, RG functions * 11: Renormalization of local polynomials. Short distance expansion * 12: Relativistic fermions: Introduction * 13: Symmetries, chiral symmetry breaking and renormalization * 14: Critical phenomena: General considerations. Mean-field theory * 15: The renormalization group approach: The critical theory near dimension 4 * 16: Critical domain: Universality, "-expansion * 17: Critical phenomena: Corrections to scaling behaviour * 18: O(N)-symmetric vector models for N large * 19: The non-linear ?-model near two dimensions: Phase structure * 20: Gross-Neveu-Yukawa and Gross-Neveu models * 21: Abelian gauge theories: The framework of quantum electrodynamics * 22: Non-Abelian gauge theories: Introduction * 23: The Standard Model of fundamental interactions * 24: Large momentum behaviour in quantum field theory * 25: Lattice gauge theories: Introduction * 26: BRST symmetry, gauge theories: Zinn-Justin equation and renormalization * 27: Supersymmetric quantum field theory: Introduction * 28: Elements of classical and quantum gravity * 29: Generalized non-linear ?-models in two dimensions * 30: A few two-dimensional solvable quantum field theories * 31: O(2) spin model and Kosterlitz-Thouless's phase transition * 32: Finite-size effects in field theory. Scaling behaviour * 33: Quantum field theory at finite temperature: Equilibrium properties * 34: Stochastic differential equations: Langevin, Fokker-Planck equations * 35: Langevin field equations, properties and renormalization * 36: Critical dynamics and renormalization group * 37: Instantons in quantum mechanics * 38: Metastable vacua in quantum field theory * 39: Degenerate classical minima and instantons * 40: Perturbative expansion at large orders * 41: Critical exponents and equation of state from series summation * 42: Multi-instantons in quantum mechanics * Bibliography * Index
* Preface * 1: Gaussian integrals. Algebraic preliminaries * 2: Euclidean path integrals and quantum mechanics * 3: Quantum mechanics: Path integrals in phase space * 4: Quantum statistical physics: Functional integration formalism * 5: Quantum evolution: From particles to fields * 6: The neutral relativistic scalar field * 7: Perturbative quantum field theory: Algebraic methods * 8: Ultraviolet divergences: Effective quantum field theory * 9: Introduction to renormalization theory and renormalization group * 10: Dimensional continuation, regularization. Minimal subtraction, RG functions * 11: Renormalization of local polynomials. Short distance expansion * 12: Relativistic fermions: Introduction * 13: Symmetries, chiral symmetry breaking and renormalization * 14: Critical phenomena: General considerations. Mean-field theory * 15: The renormalization group approach: The critical theory near dimension 4 * 16: Critical domain: Universality, "-expansion * 17: Critical phenomena: Corrections to scaling behaviour * 18: O(N)-symmetric vector models for N large * 19: The non-linear ?-model near two dimensions: Phase structure * 20: Gross-Neveu-Yukawa and Gross-Neveu models * 21: Abelian gauge theories: The framework of quantum electrodynamics * 22: Non-Abelian gauge theories: Introduction * 23: The Standard Model of fundamental interactions * 24: Large momentum behaviour in quantum field theory * 25: Lattice gauge theories: Introduction * 26: BRST symmetry, gauge theories: Zinn-Justin equation and renormalization * 27: Supersymmetric quantum field theory: Introduction * 28: Elements of classical and quantum gravity * 29: Generalized non-linear ?-models in two dimensions * 30: A few two-dimensional solvable quantum field theories * 31: O(2) spin model and Kosterlitz-Thouless's phase transition * 32: Finite-size effects in field theory. Scaling behaviour * 33: Quantum field theory at finite temperature: Equilibrium properties * 34: Stochastic differential equations: Langevin, Fokker-Planck equations * 35: Langevin field equations, properties and renormalization * 36: Critical dynamics and renormalization group * 37: Instantons in quantum mechanics * 38: Metastable vacua in quantum field theory * 39: Degenerate classical minima and instantons * 40: Perturbative expansion at large orders * 41: Critical exponents and equation of state from series summation * 42: Multi-instantons in quantum mechanics * Bibliography * Index
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