2007•American Journal of PhysicsOpen access

Spontaneous symmetry breaking in quantum mechanics

Jasper van Wezel, Jeroen van den Brink

Abstract

We present a mathematically simple procedure to explain spontaneous symmetry breaking in quantum systems. The procedure is applicable to a wide range of models and can be easily used to explain the existence of a symmetry broken state in crystals, antiferromagnets, and even superconductors. It has the advantage that it automatically brings to the fore the main players in spontaneous symmetry breaking: the symmetry-breaking field, the thermodynamic limit, and the global excitations of a “thin” spectrum.

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Key concepts: Physics, Spontaneous symmetry breaking, Explicit symmetry breaking, Symmetry breaking, Symmetry (geometry), Global symmetry, Chiral symmetry breaking, Quantum mechanics