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1. Goldstone Boson

   Linked via "$\sigma$-model"

   Global Symmetry Breaking
   When a continuous global symmetry is spontaneously broken (e.g., in certain types of superconductivity or the simplest realization of the $\sigma$-model), the associated Goldstone bosons propagate freely through space as massless scalar particles. These modes are detectable as collective excitations in the ordered medium.
   Local Symmetry Breaking: The Higgs Mechanism