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This monograph integrates unitary symmetry and combinatorics, showing in great detail how the coupling of angular momenta in quantum mechanics is related to binary trees, trivalent trees, cubic graphs, MacMahon's master theorem, and other basic combinatorial concepts. A comprehensive theory of recoupling matrices for quantum angular momentum is developed. For the general unitary group, polynomial forms in many variables called matrix Schur functions have the remarkable property of giving all irreducible representations of the general unitary group and are the basic objects of study. The structure of these irreducible polynomials and the reduction of their Kronecker product is developed in detail, as is the theory of tensor operators.

Combinatorial analysis. --- Eightfold way (Nuclear physics) --- Unitary symmetry --- Group theory --- Particles (Nuclear physics) --- Combinatorics --- Algebra --- Mathematical analysis --- Analyse combinatoire. --- Symétrie unitaire. --- Symétrie unitaire.

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This new edition of Prof. Strocchi's well received primer on rigorous aspects of symmetry breaking presents a more detailed and thorough discussion of the mechanism of symmetry breaking in classical field theory in relation with the Noether theorem. Moreover, the link between symmetry breaking without massless Goldstone bosons in Coulomb systems and in gauge theories is made more explicit in terms of the delocalized Coulomb dynamics. Furthermore, the chapter on the Higgs mechanism has been significantly expanded with a non-perturbative treatment of the Higgs phenomenon, at the basis of the standard model of particle physics, in the local and in the Coulomb gauges. Last but not least, a subject index has been added and a number of misprints have been corrected. From the reviews of the first edition: The notion of spontaneous symmetry breaking has proven extremely valuable, the problem is that most derivations are perturbative and heuristic. Yet mathematically precise versions do exist, but are not widely known. It is precisely the aim of his book to correct this unbalance. - 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. It can be recommended to physicists as well and, of course, for physics/mathematics libraries. J.-P. Antoine, Physicalia 28/2, 2006 Strocchi's main emphasis is on the fact that the loss of symmetric behaviour requires both the non-symmetric ground states and the infinite extension of the system. It is written in a pleasant 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 In these notes the author explores the phenomenon of spontaneous symmetry breaking as it arises in classical and quantum systems. 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 .

Broken symmetry (Physics) --- Symétrie brisée (Physique) --- Atomic Physics --- Physics - General --- Physics --- Physical Sciences & Mathematics --- Symmetry breaking (Physics) --- Physics. --- Topological groups. --- Lie groups. --- Quantum field theory. --- String theory. --- Quantum physics. --- Elementary particles (Physics). --- Mathematical Methods in Physics. --- Elementary Particles, Quantum Field Theory. --- Topological Groups, Lie Groups. --- Quantum Field Theories, String Theory. --- Quantum Physics. --- Symmetry (Physics) --- Mathematical physics. --- Quantum theory. --- Topological Groups. --- Groups, Topological --- Continuous groups --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Mechanics --- Thermodynamics --- Physical mathematics --- Mathematics --- Models, String --- String theory --- Nuclear reactions --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Elementary particles (Physics) --- High energy physics --- Nuclear particles --- Nucleons --- Nuclear physics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics