Quantum mechanical histories and the Berry phase

TL;DR

This paper explores the intrinsic link between the Berry phase and the probabilistic structure of quantum mechanics within the histories framework, highlighting its foundational role in decoherence and temporal quantum structures.

Contribution

It demonstrates that the Berry phase is fundamental to the decoherence functional in histories-based quantum theories, revealing a novel temporal structure.

Findings

Berry phase is linked to quantum probabilistic structure

Berry phase is a core component of the decoherence functional

Histories approach reveals new temporal quantum structures

Abstract

We elaborate on the distinction between geometric and dynamical phase in quantum theory and show that the former is intrinsically linked to the quantum mechanical probabilistic structure. In particular, we examine the appearance of the Berry phase in the consistent histories scheme and establish that it is the basic building block of the decoherence functional. These results are consequences of the novel temporal structure of histories-based theories.