ランダムウォークからランダム行列まで（テキスト）<br>From Random Walks to Random Matrices (Oxford Graduate Texts)

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ランダムウォークからランダム行列まで（テキスト）
From Random Walks to Random Matrices (Oxford Graduate Texts)

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  • 製本 Paperback:紙装版/ペーパーバック版／ページ数 544 p.
  • 言語 ENG
  • 商品コード 9780192856968
  • DDC分類 530.1

Full Description

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.

Contents

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