The accidental flatness constraint does not mean a wrong classical limit

TL;DR

This paper explains why the accidental flatness constraint in covariant loop quantum gravity is not problematic, by comparing it to similar constraints in simple systems' transition amplitudes.

Contribution

It demonstrates that the flatness constraint is harmless by illustrating its analogy with accidental constraints in simpler systems.

Findings

The flatness constraint appears in certain quantum gravity limits.

Analogous constraints occur in simple systems' transition amplitudes.

The constraint does not imply a fundamental inconsistency.

Abstract

We shed some light on the reason why the accidental flatness constraint appears in certain limits of the amplitudes of covariant loop quantum gravity. We show why this constraint is harmless, by displaying how analogous accidental constraints appear in transition amplitudes of simple systems, when certain limits are considered.