An Algebraic Framework for the Many-Body Problem

Abstract

The purpose of this chapter is to develop a framework for the description and study of hamiltonians having a many-channel structure. The term “many-channel” is used here in a rather vague sense: we are thinking of systems consisting of a (large, but finite) number of components which could interact in a complicated way but could also behave independently (i.e. the interaction between some components could be turned off). So, to the “total hamiltonian” H one should be able to associate a collection of “sub-hamiltonians” H _a which, in some sense, should be simpler than H, and then one should construct the spectral and scattering theory of H in terms of the family {H _a}.