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arXiv · 1001.5212

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

Tomas Brauner
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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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Tomas Brauner. 2010-04-06. Spontaneous Symmetry Breaking and Nambu-Goldstone Bosons in Quantum Many-Body Systems. https://doi.org/10.3390/sym2020609

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