Symmetries of decoherence functionals

The basic ingredients of the open-quotes consistent historiesclose quotes approach to quantum theory are a space scr(UP) of open-quotes history propositionsclose quotes and a space scr(D) of open-quotes decoherence functionals.close quotes In this article we consider such history quantum theories in the case where scr(UP) is given by the set of projectors scr(P)(scr(V)) on some Hilbert space scr(V). Using an analog of Wigner close-quote s theorem in the context of history quantum theories proven earlier, we develop the notion of a open-quotes symmetry of a decoherence functionalclose quotes and prove that all such symmetries form a group which we call open-quotes the symmetry group of a decoherence functional.close quotes We calculate for the case of standard quantum mechanics emdash when looked at from the perspective of the history program emdash some of these symmetries explicitly and relate them to some discussions that have appeared previously. copyright 1997 American Institute of Physics