It has also been described as the gauge boson that appears when the free electrons’ Lagrangian in the crystal is requested to be locally gauge invariant with respect to T ( 3 ), the group of the infinitesimal spatial translations. In crystalline solids the acoustic phonon is known to be the frequency-gapless Goldstone boson emerging from the spontaneous breaking of the continuous Galilean symmetry induced by the crystal lattice.
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