Stochastically and Intrinsically Extended Non-relativistic Quantum Particles

Stochastically and intrinsically extended non relativistic quantum particles are described by combining the ideas of a stochastic quantum theory and a quantum functional theory. The former relates the extension to imperfect real measurements while the latter considers it as intrinsic. Physical states, Positive-Operator-Valued measures connected to measurement, and propagators are given and discussed. The stochastic theory is sufficient when the bilocal field describing the particle has a product form.