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

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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49 pages, 2 pdf figures; v2: short discussion of pseudo-NG bosons and some references added + other minor corrections, version

Scientific paper

10.3390/sym2020609

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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