Abstract A rigorous formulation of the boson method in superconductivity is presented. Assuming the local gauge invariance and presence of a phase‐dependent order parameter and utilizing the path‐integral formalism, we derive a set of macroscopic equations which control all the superconducting states. These equations are model‐independent. They contain certain functions and parameters which should be calculated for a given model. Using this rigorous formulation, we study what kind of approximations are involved in the usual formulation of the boson method and how these approximations can be improved.
A detailed proof is given for the validity of substituting a
c number for the zero-momentum-state operators in the quantum-field-theory approach to the many-boson problem at a finite temperature. We use a modification of the method of Kromminga and Bolsterli, and add slightly to their work for the ground-state case. The case in which the bosons which condense are themselves composite particles, as in superconductivity, is treated in this method by the artifice of coupling to a fictitious elementary boson and then letting the coupling become infinitely weak; the self-consistent formulation of Schrieffer for superconductivity can be obtained in this way.