Symmetry Breaking

The intriguing mechanism of spontaneous symmetry breaking is a powerful innovative idea at the basis of most of the recent developments in theoretical physics, from statistical mechanics to many-body theory to elementary particles theory; for infinitely extended systems a symmetric Hamiltonian can account for non symmetric behaviours, giving rise to non symmetric realizations of a physical system.

In the first part of this book, devoted to classical field theory, such a mechanism is explained in terms of the occurrence of disjoint sectors and their stability properties and of an improved version of the Noether theorem.

For infinitely extended quantum systems, discussed in the second part, the mechanism is related to the occurrence of disjoint pure phases and characterized by a symmetry breaking order parameter, for which non perturbative criteria are discussed, following Wightman, and contrasted with the standard Goldstone perturbative strategy. The Goldstone theorem is discussed with a critical look at the hypotheses that emphasizes the crucial role of the dynamical delocalization induced by the interaction range. The Higgs mechanism in local gauges is explained in terms of the Gauss law constraint on the physical states. The mathematical details are kept to the minimum required to make the book accessible to students with basic knowledge of Hilbert space structures. Much of the material has not appeared in other textbooks.

• Goldstone Theorem
• Higgs Mechanism
• Spontaneous Symmetry Breaking
• Theoretical physics
• gauge theory

From the reviews:

This little book is a welcome addition to the literature on symmetries in physics. 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. The aim of Strocchi, however, is physics, not mathematics: at each step he strongly emphasizes the physical meaning and motivation of the various notions introduced. This results in a pleasant book, with an origninal structure (clearly stemming from the lectures on which the book is based).

Physicalia Vol 28/2, 2006

The mathematically oriented graduate student will certainly benefit from this thorough, rigorous and detailed investigation. - Zentralblatt MATH, 2006

The book is based on lectures given over a number of years. It is written in a pleasing style at a level suitable for graduate students in theoretical physics. While mathematically proper, it is not forbidding for a physics readership; the author is always aware this subject is a branch of physics. It should make profitable reading for many theoretical physicists. - L.H. Ryder, J. Phys. A, 38 (2005) 9719-9730

Altogether, we have here a book that fills a conspicous gap in the literature, and it does it rather well. It could also be a good basis for a graduate course in mathematical physics. It can be recommended to physicists and mathematicians as well and, of course, for physics/mathematics libraries.- J.-P. Antoine, Physicalia 28/2, 2006

"In these notes from lectures given at various occasions, the author explores the phenomenon of spontaneous symmetry breaking as it arises in classical and quantum systems. … The mathematically oriented graduate student will certainly benefit from this thorough, rigorous and detailed investigation." (Gert Roepstorff, Zentralblatt MATH, Vol. 1075,2006)

"Spontaneous symmetry breaking is often explained as due to a non-symmetrical ground state. … Throughout this book practical physical examples are given … . The treatment should be commended for the care with which many woolly notions lurking in the literature of the subject are exposed and corrected. … it will certainly amply repay the effort for those that invest some time in this excellent book. … this is the type of book that many graduate students in the subject would much benefit by owning." (S. L. Altmann, Contemporary Physics, Vol. 47 (1), 2006)

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