Quantum temporal logic and decoherence functionals in the histories approach to generalised quantum theory

TL;DR

This paper explores how quantum temporal logic and decoherence functionals can serve as a mathematical framework for generalized quantum theory based on histories, highlighting properties that connect classical and quantum systems.

Contribution

It develops the mathematical structure of quantum temporal logic and analyzes properties of decoherence functionals within the histories approach to quantum theory.

Findings

Properties of decoherence functionals reflect classical system topology

Quantum temporal logic provides a natural framework for histories-based quantum theory

Analysis supports Gell-Mann and Hartle's generalized quantum theory proposal

Abstract

We analyse and develop the recent suggestion that a temporal form of quantum logic provides the natural mathematical framework within which to discuss the proposal by Gell-Mann and Hartle for a generalised form of quantum theory based on the ideas of histories and decoherence functionals. Particular stress is placed on properties of the space of decoherence functionals, including one way in which certain global and topological properties of a classical system are reflected in a quantum history theory.