Algebra of Effects in the Formalism of Quantum Mechanics on Phase Space as an M. V. and a Heyting Effect Algebra

摘要

We prove that the algebra of effects in the phase space formalism of quantum mechanics forms an M. V. effect algebra and moreover a Heyting effect algebra. It contains no nontrivial projections. We equip this algebra with certain nontrivial projections by passing to the limit of the quantum expectation with respect to any density operator.