Condensed phase of converting boson-fermion mixtures

Theory of a condensed state of hybridised bosons and fermions is developed. Normal and anomalous Green's functions are obtained diagrammatically and analytically using the Hamiltonian of the boson-fermion model (BFM). A pairing of bosons analogous to the Cooper pairing of fermions is found. There are three coupled condensates in the model, described by the off-diagonal single-particle boson, pair-fermion and pair-boson fields. The Gor'kov expansion in the strength of the order parameter near the transition yields no linear homogeneous term in the Ginzburg-Landau equation, and the infinite Levanyuk-Ginzburg parameter, Gi, which indicates that previous mean-field discussions of BFM are flawed.