Formalism and applications of decohering histories in quantum mechanics

Roland L. Omnes

Marcelo Losada, Olímpia Lombardi

Murray Gell‐Mann, James B. Hartle

We continue our efforts to understand, within the framework of the quantum mechanics of the universe as a whole, the quasiclassical realm of familiar experience as a feature emergent from the Hamiltonian of the elementary particles and the initial condition of the universe. Quantum mechanics assigns probabilities to exhaustive sets of alternative decoherent histories of the universe. We introduce and define the notion of strong decoherence. We replace the notion of maximal sets of alternative decohering histories by defining the more useful concept of "full" sets of alternative strongly decohering histories. These full sets fall into equivalence classes each of which is characterized by a basis in Hilbert space. Finally we describe our continuing efforts to find measures of classicality --- measures that could be applied to such full sets of alternative strongly decohering so as to characterize a quasiclassical realm.

J. J. Halliwell

Eric D. Chisolm

I briefly review the "decohering histories" or "consistent histories" formulation of quantum theory, due to Griffiths, Omnès, and Gell-Mann and Hartle (and the subject of my graduate work with George Sudarshan). I also sift through the many meanings that have been attached to decohering histories, with an emphasis on the most basic one: Decoherence of appropriate histories is needed to establish that quantum mechanics has the correct classical limit. Then I will describe efforts to find physical mechanisms that do this. Since most work has focused on density matrix versions of decoherence, I'll consider the relation between the two formulations, which historically has not been straightforward. Finally, I'll suggest a line of research that would use recent results by Sudarshan to illuminate this aspect of the classical limit of quantum theory.

J. Weyers