From Random Walks to Random Matrices

Erscheinungsjahr 2019
ISBN: 978-0-19-878775-4
Verlag: Oxford University Press

Buch, Englisch, 544 Seiten, Format (B × H): 174 mm x 284 mm, Gewicht: 1190 g

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.

Autoren/Hrsg.

Zinn-Justin, Jean

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Physik Quantenphysik Hochenergiephysik
• Naturwissenschaften Physik Quantenphysik Radioaktivität
• Naturwissenschaften Physik Quantenphysik Teilchenphysik

Inhaltsverzeichnis

- 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

Über Autor(innen)

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.