Spontaneous Symmetry Breaking and Nambu–Goldstone Bosons in Quantum Many-Body Systems

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 manifesta...

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Bibliographic Details
Published in:Symmetry (Basel) 2010-06, Vol.2 (2), p.609-657
Main Author: Brauner, Tomáš
Format: Article
Language:English
Subjects:
effective field theory
Nambu–Goldstone bosons
spontaneous symmetry breaking
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Summary: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.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym2020609