Difference posets and the histories approach to quantum theories (Q1891469)

Difference posets (D-posets) are generalizations of orthomodular posets as well as of sets of all effects modelling event structures of physical systems. Gell-Mann and Hartle postulated a new approach to quantum theory in which the notion of so-called histories plays a fundamental role. In the present paper homogeneous histories are modelled by finite sequences of elements of a D-poset. Under certain assumptions the set of all histories admits the structure of a D-poset which can be obtained by constructing a direct limit of a directed system of finite tensor products of D-posets. Since effects represent unsharp measurements, by the mentioned approach ``unsharp'' histories are obtained.