On the analogy between superconductivity and chiral symmetry breakdown in the Coulomb gauge

Abstract

We study spontaneously broken gauge theories which do not explicitly involve boson fields. Our work was motivated by, and justifies, some recent results pointing to a deep analogy between particle physics and superconductivity. Thus we compare in detail the BCS theory of superconductivity, including Coulomb effects, with its relativistic generalization in the Coulomb gauge. The structure of the resulting equations is identical in both cases. The unity is best appreciated in terms of the Schwinger mechanism which leads to plasma oscillations in superconductivity and to massive spin-one particles in the relativistic case. The physical operator densities, such as charge and current densities, differ from those found by other authors concerned with the problem of gauge invariance.