The new edition of this 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. A subject index has been added and a number of misprints have been corrected.
Table of ContentsSymmetry 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.- 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.- Quantum Fields at Non-zero Temperature.- Breaking of Continuous Symmetries. Goldstone’s Theorem.- The Goldstone Theorem at Non-zero Temperature.- The Goldstone Theorem for Relativistic Local Fields.- An Extension of Goldstone Theorem to Non-symmetric Hamiltonians.- Symmetry Breaking in Gauge Theories.- Erratum.- Erratum.