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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
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  • $\begingroup$ 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. $\endgroup$ – Peter Kravchuk May 13 at 18:54

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