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For certain classes of space(time)s embeddable in a higher dimensional flat space(time), it appears possible to compute the minimally coupled massless scalar Green's function in the former by convolving its cousin in the latter with an appropriate scalar charge density.
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R. Szmytkowski, “Closed forms of the Green’s function and the generalized Green’s function for the Helmholtz operator on the N-dimensional unit sphere,” J. Phys. A: Math. Theor. 40 995 (2007)
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M. Spradlin, A. Strominger and A. Volovich, “Les Houches lectures on de Sitter space,” hep-th/0110007
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2013
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