Dynamics and Effective Actions of BCS Superconductors

We derive effective dynamical theories for metals and BCS superconductors, based on the effective action formalism. Both the metallic regime $T\gtrsim T_{C}$ and the superconducting regime $T\ll T_{C}$ are studied in the clean and dirty limit. Furthermore, we consider the effect of particle-hole asymmetry in the band structure. Using gauge invariance, the electrodynamics of the problem is formulated in a transparent way. The effective actions are useful starting points for treating dynamical problems involving BCS superconductors.