Bohrification of local nets

TL;DR

This paper extends the Bohrification approach from quantum mechanics to algebraic quantum field theory, constructing a presheaf of quantum phase spaces to analyze locality through ringed topos descent conditions.

Contribution

It introduces a method to represent quantum field theory nets as presheaves of ringed toposes, linking locality to descent conditions in this new framework.

Findings

Quantum field theory nets can be modeled as presheaves of ringed toposes.

Locality corresponds to descent conditions in the presheaf structure.

The approach generalizes Bohrification to a field-theoretic context.

Abstract

Recent results by Spitters et. al. suggest that quantum phase space can usefully be regarded as a ringed topos via a process called Bohrification. They show that quantum kinematics can then be interpreted as classical kinematics, internal to this ringed topos. We extend these ideas from quantum mechanics to algebraic quantum field theory: from a net of observables we construct a presheaf of quantum phase spaces. We can then naturally express the causal locality of the net as a descent condition on the corresponding presheaf of ringed toposes: we show that the net of observables is local, precisely when the presheaf of ringed toposes satisfies descent by a local geometric morphism.