# Why is it that the equation of a massless scalar field *must* be conformal invariant?

I'm reading a paper [1], p.111 where it is said that:

However, the equation of scalar field with zero mass must be conformal invariant while equation $$\square\varphi=0$$ does not satisfy this requirement by any means. The conformal invariant equation is: $$\square \varphi + \frac{n-2}{4(n-1)}R\varphi = 0$$ where $$R$$ is the scalar curvature of space-time and $$n$$ is its dimensionality.

Question: why is it that the equation of a massless scalar field must be conformal invariant?

This question is related to this other question: https://mathoverflow.net/q/270088/

• [1] : Quantum theory of scalar field in de Sitter space-time, N. A. Chernikov and E. A. Tagirov, 1968
• I would say that this perhaps not much more than a way to define the word "massless" in curved space. But I am curious if anyone else has an independent definition. – Peter Kravchuk May 13 at 18:54