From Random Walks to Random Matrices

Jean Zinn-Justin (Scientific Advisor, Scientific Advisor, CEA, Paris-Saclay)

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English

Oxford University Press
09 March 2022

Series: Oxford Graduate Texts

Theoretical physics is a cornerstone of modern physics and provides a foundation for all modern quantitative science. It aims to describe all natural phenomena using mathematical theories and models, and in consequence develops our understanding of the fundamental nature of the universe. This books offers an overview of major areas covering the recent developments in modern theoretical physics. Each chapter introduces a new key topic and develops the discussion in a self-contained manner. At the same time the selected topics have common themes running throughout the book, which connect the independent discussions. The main themes are renormalization group, fixed points, universality, and continuum limit, which open and conclude the work.

The development of modern theoretical physics has required important concepts and novel mathematical tools, examples discussed in the book include path and field integrals, the notion of effective quantum or statistical field theories, gauge theories, and the mathematical structure at the basis of the interactions in fundamental particle physics, including quantization problems and anomalies, stochastic dynamical equations, and summation of perturbative series.

By: Jean Zinn-Justin (Scientific Advisor Scientific Advisor CEA Paris-Saclay)
Imprint: Oxford University Press
Country of Publication: United Kingdom
Dimensions: Height: 245mm, Width: 172mm, Spine: 25mm
Weight: 1.024kg
ISBN: 9780192856968
ISBN 10: 0192856960
Series: Oxford Graduate Texts
Pages: 544
Publication Date: 09 March 2022
Audience: College/higher education , Primary
Format: Paperback
Publisher's Status: Active

1: The random walk: universality and continuum limit 2: Functional integration: from path to field integrals 3: The essential role of functional integrals in modern physics 4: From infinites in QED to the general renormalization group 5: Renormalization group: From a general concept to numbers 6: Critical phenomena: the field theory approach 7: Stability of RG fixed points and decay of correlations 8: Quantum field theory: an effective theory 9: The non-perturbative renormalization group 10: O(N) vector model in the ordered phase: Goldstone modes 11: Gauge invariance and gaude fixing 12: The discovery of the Higgs boson: a major achievement and a problem 13: Quantum Chromodynamics (QCD): A non-Abelian gauge theory 14: Non-Abelian gauge theories: renormalization and Zinn-Justin equation 15: Quantum field theory: asymptotic safety 16: Symmetries: from classical to quantum field theories 17: Quantum anomalies: A few physics applications 18: Periodic semi-classical vacuum, instantons and anomalies 19: Field theory in a finite geometry: finite size scaling 20: The weakly interacting Bose gas at the critical temperature 21: Quantum field theory at finite temperature 22: From random walk to critical dynamics 23: Field theory: Peturbative expansion and summation methods 24: Hyper-asymptotic expansions and instantons 25: Renormalization group approach to matric models

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 French Journal de Physique, Nuclear Physics B, Journal of Physics A, and the New Journal of Physics.