THE STRUCTURE OF DECOHERENCE FUNCTIONALS FOR VON-NEUMANN QUANTUM HISTORIES

Gell-Mann and Hartle have proposed a significant generalization of quantum theory in which decoherence functionals perform a key role. Isham-Linden-Schreckenberg have given a penetrating analysis of decoherence functionals for L(H), where H is finite dimensional (dimension greater than 2). In this note their conjecture on the significance of boundedness is verified. In particular, it is shown that when d is a bounded decoherence functional associated with a von Neumann algebra A, then, provided A has no direct summand of type I-2, d can be represented as the difference between semi-innerproducts on A. (C) 1995 American Institute of Physics.