Zero Modes and Displacement Symmetry in Electrodynamics

Abstract

The global residual gauge symmetry of electrodynamics, the displacement symmetry, is discussed within the Weyl-gauge formulation and used to characterize different phases of the Maxwell field coupled to matter. Unlike other global symmetries, the displacement symmetry, in the absence of interactions or in the weak coupling regime, is realized in the Nambu-Goldstone mode. The displacement symmetry will be shown to be realized in the Wigner-Weyl mode in the plasma and superconducting states; this discussion develops a novel perspective of the plasma oscillations. Other examples are the states of the Schwinger model and the non-perturbative phase of the Abelian Higgs model. The Higgs mechanism is interpreted as formation of a phase with a high degree of symmetry. Finite photon mass and shielding of external fields will be recognized as the characteristic properties of these symmetric phases.