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

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Author(s): Tomáš Brauner

Journal: Symmetry
ISSN 2073-8994

Volume: 2;
Issue: 2;
Start page: 609;
Date: 2010;
Original page

Keywords: spontaneous symmetry breaking | Nambu–Goldstone bosons | effective field theory

ABSTRACT
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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