Symmetries of history quantum theories and decoherence functionals

Recently, Schreckenberg investigated symmetries in the context of history q uantum theories. In the case that the space of histories is given by the se t of projectors on some finite dimensional Hilbert space he obtained, first , a complete characterization of all physical symmetries of history quantum theories - an analog of Wigner's theorem - and, second, a complete mathema tical characterization of symmetries of single decoherence functionals. In this paper we extend Schreckenberg's results to the case where the underlyi ng space of histories is given by the set of projectors on some infinite di mensional Hilbert space. (C) 1998 American Institute of Physics. [S0022-248 8(98)02011- 8].