Perturbation expansion for a Fermi superfluid .1. Basic formalism and angular momentum.

A theory of a Fermi superfluid is formulated based on the condensate wave function of the configuration space. First, two basic ingredients are extracted from the wave function, i.e. the effective condensate wave function upsilon(x(1),x(2)) and the quasiparticle field gamma(x) with x denoting the space and spin coordinates tau alpha. After transforming a Hamiltonian into a normal-ordered product of gamma, a perturbation expansion with respect to the quasiparticle interaction is formulated for both the thermodynamic potential Omega and the one-particle density matrix rho. The thermodynamic potential thus obtained includes the normal-state expression of Luttinger and Ward as the limit of upsilon-->0. The density matrix is written as a sum of the coherent part rho((c))) and the quasiparticle part rho((q)), where rho((c)) is expressed only with respect to upsilon(x(1),x(2)). It is shown that upsilon and gamma are responsible for the coherent and thermodynamic properties respectively. Thus the present formalism gives a microscopic foundation for the two-fluid model. Connections with the Gor'kov equations and the Bogoliubov-de Gennes equations are also clarified. It is found that the one-particle density matrices of those formalisms are not equivalent to rho of the present formalism. The origin of the angular momentum paradox of He-3-A is traced to this difference.