Self-consistent approximations in the theory of triplet pairing superfluidity in3He

Abstract

A self-consistent and “spin-conserving” approximation scheme in the theory of triplet pairing superfluidity in3He is developed in terms of normal and anomalous Gor'kov Green's functions and the antisymmetrized interaction function. Both the normal and anomalous self-energy parts must be derived from the same diagrammatic approximation to a certain functional Φ, which in turn can be obtained from an approximation to the thermodynamic potential. With the help of this prescription the particle-holeT-matrix approximation to the normal system is generalized by taking into account that in the superfluid state the spin fluctuations are propagated also by pairs of anomalous Green's functions. The resulting equations for the components (with respect to the Pauli matrices) of the normal and anomalous self-energy parts and theT-matrix are treated in a self-consistent way. Explicit expressions for the effective interaction kernels occurring in the gap equations are given in terms of normal and anomalous “bare particle-hole susceptibilities.” The results are discussed in connection with the original theory of Layzer and Fay and the recent one of Anderson and Brinkman.