From random walks to random matrices : selected topics in modern theoretical physics / Jean Zinn-Justin (IRFU/CEA, Paris-Saclay University and French Academy of Sciences).
Includes bibliographical references (pages 501-519) and index.
Contents:
The random walk: Universality and continuum limit -- Functional integration: From path to field integrals -- The essential role of functional integrals in modern physics -- From infinities in QED to the general renormalization group -- Renormalization Group: From a general concept to numbers -- Critical phenomena: The field theory approach -- Stability of renormalization group fixed points and decay of correlations -- Quantum field theory: An effective theory -- The non-perturbative renormalization group -- O(N) vector model in the ordered phase: Goldstone modes -- Gauge invariance and gauge fixing -- The Higgs boson: A major discovery and a problem -- Quantum chromodynamics: A non-Abelian gauge theory -- From BRST symmetry to the Zinn-Justin equation -- Quantum field theory: Asymptotic safety -- Symmetries: From classical to quantum field theories -- Quantum anomalies: A few physics applications -- Periodic semi-classical vacuum, instantons and anomalies -- Field theory in a finite geometry: Finite size scaling -- The weakly interacting Bose gas at the critical temperature -- Quantum field theory at finite temperature -- Field theory: Peturbative expansion and summation methods -- Hyper-asymptotic expansions and instantons -- Renormalization group approach to matrix models.
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