Journal
SYMMETRY-BASEL
Volume 2, Issue 2, Pages 609-657Publisher
MDPI
DOI: 10.3390/sym2020609
Keywords
spontaneous symmetry breaking; Nambu-Goldstone bosons; effective field theory
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Funding
- ExtreMe Matter Institute EMMI in the framework of the Helmholtz Alliance Program of the Helmholtz Association [HA216/EMMI]
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Spontaneous symmetry breaking is a general principle that constitutes the underlying concept of a vast number of physical phenomena ranging from ferromagnetism and superconductivity in condensed matter physics to the Higgs mechanism in the standard model of elementary particles. I focus on manifestations of spontaneously broken symmetries in systems that are not Lorentz invariant, which include both nonrelativistic systems as well as relativistic systems at nonzero density, providing a self-contained review of the properties of spontaneously broken symmetries specific to such theories. Topics covered include: (i) Introduction to the mathematics of spontaneous symmetry breaking and the Goldstone theorem. (ii) Minimization of Higgs-type potentials for higher-dimensional representations. (iii) Counting rules for Nambu-Goldstone bosons and their dispersion relations. (iv) Construction of effective Lagrangians. Specific examples in both relativistic and nonrelativistic physics are worked out in detail.
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