Meissner Effect and Gauge Invariance

Abstract

It is shown from a manifestly gauge-invariant Hamiltonian that the Meissner effect can follow from an energy-gap model of superconductivity. The superconductor is described by Fröhlich's Hamiltonian and the superconducting properties at the absolute zero are determined by a method due to Bogoliubov. In the weak-coupling limit ($T_c\ll {\Theta }_D$) there is an energy gap which leads to a Meissner effect. The method of Bogoliubov is extended to apply at general temperatures and the current is calculated in the weak-coupling limit. The results are in essential agreement with those of Bardeen, Cooper, and Schrieffer.