Background Independent Field Quantization with Sequences of Gravity-Coupled Approximants

TL;DR

This paper proposes a background independent, nonperturbative scheme for quantized fields coupled with gravity, which naturally generates the correct spacetime geometry and addresses the cosmological constant problem.

Contribution

It introduces a sequence-based regularization approach for quantum fields in gravity, enabling self-consistent backreaction and a natural emergence of spacetime geometry.

Findings

The approach removes the cosmological constant problem in the continuum limit.

Application to de Sitter space offers a natural interpretation of Bekenstein-Hawking entropy.

Demonstrates the scheme's effectiveness on Gaussian scalar fields in symmetric spacetimes.

Abstract

We outline, test, and apply a new scheme for nonpertubative analyses of quantized field systems in contact with dynamical gravity. While gravity is treated classically in the present paper, the approach lends itself for a generalization to full Quantum Gravity. We advocate the point of view that quantum field theories should be regularized by sequences of quasi-physical systems comprising a well defined number of the field's degrees of freedom. In dependence on this number, each system backreacts autonomously and self-consistently on the gravitational field. In this approach, the limit which removes the regularization automatically generates the physically correct spacetime geometry, i.e., the metric the quantum states of the field prefer to "live" in. We apply the scheme to a Gaussian scalar field on maximally symmetric spacetimes, thereby confronting it with the standard approaches. As an application, the results are used to elucidate the cosmological constant problem allegedly arising from the vacuum fluctuations of quantum matter fields. An explicit calculation shows that the problem disappears if the pertinent continuum limit is performed in the improved way advocated here. A further application concerns the thermodynamics of de Sitter space where the approach offers a natural interpretation of the micro-states that are counted by the Bekenstein-Hawking entropy.