Anomaly in canonical semiclassical gravity

TL;DR

This paper demonstrates that the canonical formulation of semiclassical gravity, replacing matter terms with quantum expectation values, is inconsistent because the resulting constraints do not form a closed algebra.

Contribution

It reveals a fundamental inconsistency in the canonical approach to semiclassical gravity due to non-closure of the constraint algebra.

Findings

Constraint algebra does not close in the canonical semiclassical Einstein equation.

The inconsistency challenges the validity of the canonical semiclassical gravity framework.

Highlights the need for alternative formulations or modifications.

Abstract

We show that the canonical formulation of the semiclassical Einstein equation, where the matter terms in the constraints are replaced by expectation values of the corresponding operators in quantum states, is inconsistent due to the non-closure of the resulting constraint algebra.