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Publications of the Astronomical Society of Australia , volume =

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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.

years

2026 1 2025 1

verdicts

UNVERDICTED 2

representative citing papers

Spontaneous symmetry breaking on graphs and lattices

cond-mat.dis-nn · 2025-12-10 · unverdicted · novelty 7.0

Spontaneous symmetry breaking on graphs and lattices is controlled by the spectral dimension and generalizations of resistance distance and the Kirchhoff index.

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