On the long standing issue of an R phi(2) coupling between gravity and a massless free scalar field - Accioly, Antonio Jose [UNESP]; Aldrovandi, R. [UNESP]; Novaes, Sérgio Ferraz [UNESP]; Spehler, D. [UNESP]; Mukai, H. (Kyoto Univ, 1997)
Using 2-body trees on a flat space background, it is shown that the actions A[g, φ] = (Latin small letter esh) d4x√-g [(R/2K) + (1/2)(gμν ∂μφ∂νφ + λRφ2)] and Ā[ḡ, φ̄] = (Latin small letter esh) d4x√ - ḡ [(R̄/2k) + (1/2) ḡμν∂μφ̄∂ νφ] describe the same theory at the tree-level in this case. We also demonstrate the quantum equivalence (at one-loop) of the barred and unbarred systems for λ == -1/6 (conformal coupling).