Synaptic Algebras as Models for Quantum Mechanics

Abstract

In this survey paper, synaptic algebras are considered as suitable models for the description of quantum mechanical systems. It is shown that physically most important concepts, states and observables, can be modeled in the frame of synaptic algebras. It is shown that every element of a generalized Hermitian algebra, which is a special case of a synaptic algebra, corresponds to an observable on the OML of its projections, and a continuous functional calculus is developed. It is also shown that synaptic algebras admit type decompositions analogous to type decompositions of von Neumann algebras.