ARTICLE: Bindloss, I.P. Quantum field theory in conventional superconductors

Abstract: We review the application of the methods of quantum field theory to conventional superconductors, emphasizing the path integral approach. Zero temperature and finite temperature BCS theory is derived via a Hubbard-Strantonivich transformation. Next, superconductivity is looked at from the more general viewpoint of spontaneously broken gauge symmetry, and the most robust properties are derived from this assumption, without the need for a microscopic theory. This leads to a phenomenological discussion of Ginzberg-Landau (GL) theory and then a rigorous derivation of GL theory from the microscopic effective action. Then, the effective action is diagonalized via a Bogoliubov transformation made from the viewpoint of a unitary "rotation" of the Fermi fields. We conclude with a discussion of the crossover from BCS theory to Bose-Einstein Condensation, and discuss the application of quantum field theory to the problem of a Bose gas with repulsive short-range interactions.

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