A strongly coupled many-body system (a system of fermions confined in a shell surrounding the Fermi surface for which the variation in the single-particle kinetic energy is neglected) is defined. Some general properties of this system are obtained, in particular a criterion for permissible approximations. It is shown that a set of diagrams in which an electron of momentum and of spin ↓ interacts with many electrons of momentum and spin ↑, where does not grow too large, can be consistently extracted from the totality of graphs generated by this strongly coupled Hamiltonian. When analyzed, these lead to a ground-state and single-particle spectrum displaying the important qualitative features of a BCS superconductor.
- Received 18 January 1971
- Published in the issue dated 1 August 1971
© 1971 The American Physical Society