Symmetries of Decoherence Functionals

Abstract

The basic ingredients of the `consistent histories' approach to quantum theory are a space \UP of `history propositions' and a space \D of `decoherence functionals'. In this article we consider such history quantum theories in the case where \UP is given by the set of projectors \P(\V) on some Hilbert space \V. Using an analogue of Wigner's Theorem in the context of history quantum theories proven earlier, we develop the notion of a `symmetry of a decoherence functional' and prove that all such symmetries form a group which we call `the symmetry group of a decoherence functional'. We calculate---for the case of history quantum mechanics---some of these symmetries explicitly and relate them to some discussions that have appeared previously.Comment: Submitted to Jour.Math.Phys.; 12 pages; Latex-documen