# Diffeomorphisms and coordinate changes

In this question: Simple conceptual question conformal field theory, an answer states that the invariance of the theory under the change of coordinates is a particular case of invariance under diffeomorphisms. But, since change of coordinates are local diffeomorphisms, is this really true?

From a mathematical point of view, coordinates are not global in general and thus if the theory is invariant under (global) diffeomorphisms, it not necessary the case for local diffeomorphisms too, and so for coordinates changes.

• Terminology here is not completely uniform. "Invariance under coordinate changes" is global if we allow that the coordinates can come in many patches. "Diffeomorphism" is sometimes taken to include a change in the metric, sometimes not. Apr 4 at 9:54