Perturbation Expansions and Functional Integrals in the Theory of Superconductivity

A functional integral representation of the partition function for a superconductor is derived by conventional perturbation-theoretic techniques. The derivation involves a generalization of the ladder diagram expansion by means of a trick due to Gaudin, and the result turns out to be a variation of the functional integral derived by Hubbard. A saddle-point approximation then leads to the usual Bardeen-Cooper-Schrieffer (BCS) equations. Although this approximation is mathematically unjustified, its predictions seem to be accurate. In particular, a very literal interpretation of the saddle-point method is supported by flux-quantization experiments.