Symmetry Breaking

Symmetry Breaking

by Strocchi, F.

Type Book
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The third edition of the by now classic reference on rigorous analysis of symmetry breaking in both classical and quantum field theories adds new topics of relevance, in particular the effect of dynamical Coulomb delocalization, by which boundary conditions give rise to volume effects and to energy/mass gap in the Goldstone spectrum (plasmon spectrum, Anderson superconductivity, Higgs phenomenon). The book closes with a discussion of the physical meaning of global and local gauge symmetries and…

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Title Statements

  • Full title :Symmetry Breaking / Franco Strocchi.

Summary

The third edition of the by now classic reference on rigorous analysis of symmetry breaking in both classical and quantum field theories adds new topics of relevance, in particular the effect of dynamical Coulomb delocalization, by which boundary conditions give rise to volume effects and to energy/mass gap in the Goldstone spectrum (plasmon spectrum, Anderson superconductivity, Higgs phenomenon). The book closes with a discussion of the physical meaning of global and local gauge symmetries and their breaking, with attention to the effect of gauge group topology in QCD. From the reviews of the first edition: It is remarkable to see how much material can actually be presented in a rigorous way (incidentally, many of the results presented are due to Strocchi himself), yet this is largely ignored, the original heuristic derivations being, as a rule, more popular. - At each step he strongly emphasizes the physical meaning and motivation of the various notions introduced ... a book that fills a conspicuous gap in the literature, and does it rather well. It could also be a good basis for a graduate course in mathematical physics. J.-P. Antoine, Physicalia 28/2, 2006 Despite many accounts in popular textbooks and a widespread belief, the phenomenon is rather subtle, requires an infinite set of degrees of freedom and an advanced mathematical setting of the system under investigation. ... The mathematically oriented graduate student will certainly benefit from this thorough, rigorous and detailed investigation. G. Roepstorff, Zentralblatt MATH, Vol. 1075, 2006 From the reviews of the second edition: This second edition of Strocchi's Symmetry Breaking presents a complete, generalized and highly rigorous discussion of the subject, based on a formal analysis of conditions necessary for the mechanism of spontaneous symmetry breaking to occur in classical systems, as well as in quantum systems. ... This book is specifically recommended for mathematical physicists interested in a deeper and rigorous understanding of the subject, and it should be mandatory for researchers studying the mechanism of spontaneous symmetry breaking. S. Hajjawi, Mathematical Reviews, 2008.

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Edition Statements

  • Publication Date:2021
  • Edition:Third edition

Publication Statements

  • Publisher(s):Springer
  • Place of Publication:Berlin, Germany
  • Language:eng
  • Publication Date:2021

The Physical Object

  • Description:1 online resource (xiii, 286 pages)

Edition Identifiers

  • ISBN:9783662621660, 3662621665
  • DOI:10.1007/978-3-662-62166-0
  • oclc:on1239997588
  • LC Classification:QC174.17.S9
  • Dewey Decimal:539.7/25

Table of Contents

pt. 1. Symmetry breaking in classical systems. Symmetries of a classical system ; Spontaneous symmetry breaking ; Symmetries in classical field theory ; General properties of solutions of classical field equations ; Stable structures, Hilbert sectors, phases ; Stability under space translations. Positive energy ; Noether theorem and symmetry breaking ; Examples ; The Goldstone theorem ; Appendixes: Properties of the free wave propagator; The Cauchy problem for small times; The global Cauchy problem; The non-linear wave equation with driving team; Time independent solutions defining physical sectors -- pt. 2. Symmetry breaking in quantum systems. Quantum mechanics. Algebraic structure and states ; Fock representation ; Non-fock representations ; Mathematical description of infinitely extended quantum systems ; Physically relevant representations ; Cluster property and pure phases ; Examples ; Symmetry breaking in quantum systems ; Examples ; Constructive symmetry breaking ; Symmetry breaking in the Ising model ; Thermal states ; Fermi and bose gas at non-zero temperature ; Breaking of continuous symmetries. Goldstone's theorem ; The Goldstone theorem at non-zero temperature ; The G…

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Subjects

Broken symmetry (Physics) Symétrie brisée (Physique)

Writers

Strocchi, F.

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