Spontaneous symmetry breaking is a revolutionary new idea of thinking in terms of symmetry and the corresponding properties of physical systems. The first part of this book develops the mathematical understanding of spontaneous symmetry breaking on the basis of classical field theory. The author addresses the existence of sectors, stability, and presents an improved Noether theorem, as well as the classical counterpart of the Goldstone theorem. The second part deals with quantum systems. Here criteria for spontaneous symmetry breaking are discussed in detail as well as Goldstone's theorem, gauge theories are included, and the theorem on the Higgs mechanism is presented. The author keeps the mathematical details to the minimum required to make the book accessible to students with basic knowledge of Hilbert space structures. Much of the material appears here for the first time in book form.
Author(s): Franco Strocchi (auth.)
Series: Lecture notes in physics 643
Edition: 1
Publisher: Springer Berlin Heidelberg
Year: 2005
Language: English
Pages: 187
City: Berlin; New York
Tags: Mathematical Methods in Physics;Quantum Physics;Mathematical and Computational Physics;Elementary Particles, Quantum Field Theory
Introduction to Part I....Pages 3-6
1 Symmetries of a Classical System....Pages 7-8
2 Spontaneous Symmetry Breaking....Pages 9-11
3 Symmetries in Classical Field Theory....Pages 13-16
4 General Properties of Solutions of Classical Field Equations....Pages 17-20
5 Stable Structures, Hilbert Sectors, Phases....Pages 21-28
6 Sectors with Energy-Momentum Density....Pages 29-31
7 An Improved Noether Theorem. Spontaneous Symmetry Breaking....Pages 33-37
8 Examples....Pages 39-43
9 The Goldstone Theorem....Pages 45-49
10 Appendix....Pages 51-60
Introduction to Part II....Pages 63-66
1 Quantum Mechanics. Algebraic Structure and States....Pages 67-71
2 Fock Representation....Pages 73-79
3 Non-Fock Representations....Pages 81-87
4 Mathematical Description of Infinitely Extended Systems....Pages 89-93
5 Physically Relevant Representations....Pages 95-98
6 Cluster Property and Pure Phases....Pages 99-103
7 Examples....Pages 105-113
8 Symmetry Breaking in Quantum Systems....Pages 115-122
9 Examples....Pages 123-125
10 Constructive Symmetry Breaking....Pages 127-130
11 Symmetry Breaking in the Ising Mode....Pages 131-138
12 * Thermal States....Pages 139-150
13 Fermi and Bose Gas at Non-zero Temperature....Pages 151-157
14 Quantum Fields at Non-zero Temperature....Pages 159-160
15 Breaking of Continuous Symmetries. Goldstone’s Theorem....Pages 161-176
16 * The Goldstone Theorem at Non-zero Temperature....Pages 177-179
17 The Goldstone Theorem for Relativistic Local Fields....Pages 181-188
18 An Extension of Goldstone Theorem to Non-symmetric Hamiltonians....Pages 189-192
19 The Higgs Mechanism: A Theorem....Pages 193-196
