Particle-hole fluctuation corrections to BCS theory via functional integral techniques

The standard BCS approach to superconductivity considers only particle-particle pairing interactions, meaning that Cooper pairing arises as an instability of an otherwise well-defined Fermi surface. In a more generic situation, other interactions can compete with the Cooper instability and lead to a breakdown in the formation of a Fermi surface, which as a result changes the properties of the ground state. We explore a functional-integral method for rigorously incorporating particle-hole fluctuation corrections to the BCS theory of superconductivity. These corrections arise naturally as the result of a multi-channel Hubbard-Stratonovich decomposition of an attractive Hubbard interaction. Differences between this approach and previous models of particle-hole corrections to BCS theory are considered.