An axiomatic scheme more general than quantum theory

Abstract

An axiomatic scheme generalizing the operational approach to quantum theory is described. Only quite general axioms ensuring the existence of well-behaved probabilities are postulated. The space-time location of macroscopic apparatus interacting with the object is explicitly taken into consideration. The states and observables are defined and their time development is considered. The classification of physical processes with respect to their reversibility or irreversibility in time is given. The conditions of Lorentz and translational invariance are formulated. Linear transformations corresponding to operations on the object are introduced. In the case of reversible processes these transformations form an algebra and linear representations of the Poincaré group arise naturally. These results are, in general, invalid for irreversible processes. The position of quantum theory in the scheme described is clarified.