  We investigate the BCS and generalized BCS theories in the relativistic
quantum field theory. We select the gauge freedom as U(1), and introduce a
BCS-type effective attractive interaction. After introducing the Gor'kov
formalism and performing the group theoretical consideration of the mean
fields, we solve the relativistic Gor'kov equation and obtain the Green's
functions in analytical forms. We obtain various types of gap equations.
