A gauge invariant formulation of the B.C.S. theory of superconductivity
Oliphant, Thomas A., Jr
Doctor of Philosophy
The question of gauge invariance in the theory of the Meissner effect has been a controversial question with regard to the Bardeen, Cooper, and Schrieffer (B.C.S.) theory of superconductivity and has received considerable comment. The purpose of the present work is a reformulation of the B.C.S. theory which is gauge invariant. The central idea underlying the reformulation is the use of wave functions of cylindrical symmetry for the free electrons. By restricting ourselves to a uniform, external magnetic field, we are able to put in the magnetic field before performing the Bogoliubov transformation. This also enables us to avoid the use of perturbation theory in the treatment of the effect of the magnetic field. Therefore, the derivation of the London equation is much simpler and the effect of the magnetic field on the energy gap is included. Also, the rigidity of the superconducting ground state is exhibited more clearly.
Particle physics; Elementary particles; High energy physics