A Formalism for Generalized Quantum Mechanics

Abstract

A generalization of a non-Hilbert-space formalism, developed in two previous papers, is presented. In this generalization observables with a many-dimensional spectrum are considered. Furthermore, the fundamental mathematical tools are generalized by introducing generalized functions instead of measures. It is then proved that a physical equivalence of the present formalism with the Hilbert-space formalism can still be established.