From random walks to random matrices : selected topics in modern theoretical physics

From random walks to random matrices : selected topics in modern theoretical physics / Jean Zinn-Justin.

This text presents a collection of short, self-contained introductions to important topics in modern theoretical physics, as presented at universities worldwide in seminars (some in colloquium style) and short courses.

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Bibliographic Details
Main Author: Zinn-Justin, Jean (Author)
Format: eBook
Language:English
Published: Oxford : Oxford University Press, 2019.
Series:Oxford graduate texts.
Subjects:
Mathematical physics.
Field theory (Physics)
Quantum field theory.
Renormalization (Physics)
Quantum theory.
Statistical physics.
Physics.
physics.
SCIENCE > Energy.
SCIENCE > Mechanics > General.
SCIENCE > Physics > General.
Physics
Quantum theory
Statistical physics
Online Access:Click for online access
Table of 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 infinites in quantum electrodynamics 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
  • From random walk to critical dynamics
  • Field theory: perturbative expansion and summation methods
  • Hyper-asymptotic expansions and instantons
  • Renormalization group approach to matrix models
  • Bibliography
  • Index.

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