ABSTRACT
This chapter examines the energy of the resulting quasi-particle using the Green function technique. The field-theoretic Green function technique developed originally by Feynman, Dyson, and others for quantum electrodynamics finds extensive applications to the many body problems encountered in different branches of physics, for its proven efficacy in dealing with the dynamical effects associated with these problems. The Green function formalism is essentially a systematic time-dependent perturbation theory involving certain quantities called the Green functions or propagators. The energy-dependent Green function, G, provides great many physical information about a system, in particular the energy of the quasi-particles. Puff and Whitfield have considered the thermodynamic Green functions for the problem and found at the end of the calculation the zero-temperature limit. In the zero-temperature limit the approximate thermodynamic Green function of Mahan becomes equivalent to the intermediate coupling polaron model of Haeringen and is thus expected to give the same result as given by method of Haeringen.
