Consistency of Semiclassical Gravity

TL;DR

This paper examines the subtleties and consistency issues in the semiclassical approximation of quantum gravity, focusing on the existence of time functions, the role of anomalies, and implications for quantum field theory in various spacetime foliations.

Contribution

It clarifies the conditions under which semiclassical time functions exist and highlights the impact of anomalies on the consistency of semiclassical gravity.

Findings

Integrability conditions restrict the existence of Tomonaga-Schwinger time functions.

Central charges in matter sectors can spoil semiclassical consistency unless anomalies are canceled.

Implications for quantum field theory in flat spacetime with arbitrary foliations are discussed.

Abstract

We discuss some subtleties which arise in the semiclassical approximation to quantum gravity. We show that integrability conditions prevent the existence of Tomonaga-Schwinger time functions on the space of three-metrics but admit them on superspace. The concept of semiclassical time is carefully examined. We point out that central charges in the matter sector spoil the consistency of the semiclassical approximation unless the full quantum theory of gravity and matter is anomaly-free. We finally discuss consequences of these considerations for quantum field theory in flat spacetime, but with arbitrary foliations.