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Symmetry 2010, 2(2), 609-657; doi:10.3390/sym2020609

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

1 Institute for Theoretical Physics, Goethe University, 60438 Frankfurt am Main, Germany 2 Department of Theoretical Physics, Nuclear Physics Institute ASCR, 25068 Řež, Czech Republic
Received: 1 January 2010 / Revised: 31 March 2010 / Accepted: 6 April 2010 / Published: 7 April 2010
(This article belongs to the Special Issue Symmetry Breaking Phenomena)
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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.
Keywords: spontaneous symmetry breaking; Nambu–Goldstone bosons; effective field theory spontaneous symmetry breaking; Nambu–Goldstone bosons; effective field theory
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Brauner, T. Spontaneous Symmetry Breaking and Nambu–Goldstone Bosons in Quantum Many-Body Systems. Symmetry 2010, 2, 609-657.

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