Physical Symmetries of Quantum Histories

Abstract:

Gell-Mann and Hartle have proposed a significant generalisation of quantum theory in which decoherence functionals play a key role. Physical symmetries of quantum history systems are shown, under mild physical assumptions, to correspond to isometric Jordan *-automorphisms of the underlying von Neumann algebra. Unitary representations of groups of symmetries of quadratic forms over operator algebras are discussed and related to symmetries of decoherence functionals.