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The elastic properties of solids are described in close analogy with GeneralRelativity, by locally gauging the translational group of space-time. Electroninteractions with the crystal lattice are thus generated by enforcing fullgauge invariance, with the introduction of a gauge field. Elementaryexcitations are associated with the local gauge, contrasting to the usualinterpretation as being Goldstone bosons emerging from global symmetrybreaking. In the linear limit of the theory, the gauge field displays elasticwaves, that we identify with acoustic phonons, when the field is quantized.Coupling with the electronic part of the system yields the standardelectron-phonon interaction. If spin-orbit effects are included, unusualcouplings emerge between the strain field and the electronic spin current,leading to novel physics that may be relevant for spintronic applications.

The electron-phonon interaction from fundamental local gauge symmetries in solids