HIGHER ORDER MEASURES, GENERALIZED QUANTUM MECHANICS AND HOPF ALGEBRAS
Chryssomalis Chryssomalakos, Micho Ðurđevich
We study Sorkin's proposal of a generalization of quantum mechanics and find that the theories proposed derive their probabilities from k th order polynomials in additive measures, in the same way that quantum mechanics uses a probability bilinear in the quantum amplitude and its complex conjugate. Two complementary approaches are presented, a C* and a Hopf-algebraic one, illuminating both algebraic and geometric aspects of the problem.
arXiv:quant-ph/0309092•Modern Physics Letters A•Jan 20, 2004•3 citations