Magnetic gauge transformations in solid-state problems

Gauge transformation theory, indispensable in particle physics, is finding a role in magnetic dynamics in the solid state. It can allow for the presence of an imposed magnetic field on the quantum formulation of translational symmetry, thereby extending the range and power of Bloch theory applied to crystalline magnetic phenomena. The principle is explained and reviewed, along with comments on its application to such features as incommensurate and commensurate enumeration of states, magnetic spectra, quantum phasing and flux quantization.