Berry phase and quantum structure

TL;DR

This paper explores the fundamental role of the Berry phase in quantum mechanics, emphasizing its geometric origin in the U(1) bundle over projective Hilbert space and advocating for an ontic structural realism perspective.

Contribution

It clarifies the minimal mathematical structure needed to account for the Berry phase, highlighting the importance of the quantum bundle's curvature in quantum phenomena.

Findings

Berry phase arises from the curvature of the quantum bundle

The appropriate structure for quantum phenomena includes the U(1) bundle over projective space

Supports ontic structural realism for a realistic understanding of quantum theory

Abstract

The paper aims to spell out the relevance of the Berry phase in view of the question what the minimal mathematical structure is that accounts for all observable quantum phenomena. The question is both of conceptual and of ontological interest. While common wisdom tells us that the quantum structure is represented by the structure of the projective Hilbert space, the appropriate structure rich enough to account for the Berry phase is the U(1) bundle over that projective space. The Berry phase is ultimately rooted in the curvature of this quantum bundle, it cannot be traced back to the Hamiltonian dynamics alone. This motivates the ontological claim in the final part of the paper that, if one strives for a realistic understanding of quantum theory including the Berry phase, one should adopt a form of ontic structural realism.