Quantum mechanical N-body systems with dilatation analytic interactions are investigated. Absence of continuous singular part for the Hamiltonians is proved together with the existence of an absolutely continuous part having spectrum [2e, oo), where 2 e is the lowest many body threshold of the system. In the complement of the set of thresholds the point spectrum is discrete; corresponding bound state wave-functions are analytic with respect to the dilatation group.

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A description of the quasi-free states on a Clifford algebra and their representations is given, and we prove that the pure quasi-free states are Fock States.

We study states on Clifford algebras from the point of view of C*algebras. A criterium is given under which the odd-point functions vanish. A particular set of states, called quasi-free states is extensively studied and explicit representations are given; as an application we give an approximate calculation of the ground state of a Fermion system.