On the Classification of Decoherence Functionals

TL;DR

This paper extends the classification of decoherence functionals within the consistent histories approach to quantum mechanics, accommodating more general Hilbert spaces beyond the previously studied cases.

Contribution

It generalizes the classification theorem for decoherence functionals to include arbitrary separable or non-separable Hilbert spaces of dimension greater than two.

Findings

Extended the classification theorem to broader Hilbert spaces

Provided a more general framework for decoherence functionals

Enhanced understanding of the structure of histories in quantum mechanics

Abstract

The basic ingredients of the consistent histories approach to quantum mechanics are the space of histories and the space of decoherence functionals. In this work we extend the classification theorem for decoherence functionals proven by Isham, Linden and Schreckenberg to the case where the space of histories is the lattice of projection operators on an arbitrary separable or non-separable complex Hilbert space of dimension strictly greater than two.