Quantum stochastic models

Abstract

Quantum stochastic models are developed within the framework of a measure entity. An entity is a structure that describes the tests and states of a physical system. A measure entity endows each test with a measure and equips certain sets of states as measurable spaces. A stochastic model consists of measurable realvalued function on the set of states, called a generalized action, together with measures on the measurable state spaces. This structure is then employed to compute quantum probabilities of test outcomes. We characterize those measure entities that are isomorphic to a quantum probability space. We also show that stochastic models provide a phase space description of quantum mechanics and a realistic model of spin.