Towards Relational Quantum Field Theory

TL;DR

This paper develops a relational framework for quantum field theory on curved spacetimes, integrating quantum reference frames and indefinite causality to bridge quantum physics and general relativity.

Contribution

It introduces a novel integration theory for quantum fields with respect to quantum frames, extending operational approaches to curved spacetimes and indefinite causality.

Findings

Framework for relational quantum fields on curved backgrounds

Extension of quantum reference frames to principal bundles

Potential insights into quantum gravity and spacetime structure

Abstract

This paper presents a research program aimed at establishing relational foundations for relativistic quantum physics. Although the formalism is still under development, we believe it has matured enough to be shared with the broader scientific community. Our approach seeks to integrate Quantum Field Theory on curved backgrounds and scenarios with indefinite causality. Building on concepts from the operational approach to Quantum Reference Frames, we extend these ideas significantly. Specifically, we initiate the development of a general integration theory for operator-valued functions (quantum fields) with respect to positive operator-valued measures (quantum frames). This allows us to define quantum frames within the context of arbitrary principal bundles, replacing group structures. By considering Lorentz principal bundles, we enable a relational treatment of quantum fields on arbitrarily curved spacetimes. A form of indefinite spatiotemporality arises from quantum states in the context of frame bundles. This offers novel perspectives on the problem of reconciling principles of generally relativistic and quantum physics and on modelling gravitational fields sourced by quantum systems.