Formulation of many-body theory for composite particles

Abstract

We present a formalism for the description of many-particle systems when the particles are themselves composites of several elementary constituents. We investigate specifically the case of composites made up of two fermions, the method being easily extended to more general composites. The formalism, although its development is guided by the knowledge that there are fermion constituents in the composites, is given entirely in the composite language and requires no reference to these underlying fermions. Thus, the procedure maintains all required symmetries at every step. Composite field operators satisfying all symmetries are defined, these fields obeying neither Bose nor Fermi commutation rules, but more complicated ones. The many-composite dynamics is studied via the Green's functions formed from composite operator products. A Hartree-Fock-like approximation is introduced and leads to the generation of composite wave functions describing the distortion of the composite internal states by the presence of other composites in the system.