Higher order diagrams in quantum gravity and the continuous dimension method

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Abstract
The following three third‐order Feynman diagrams in quantum gravity are treated in the context of dimensional regularization: (a) the pure graviton triangle diagram and (b) two massless tadpole diagrams. It is shown that the graviton vertex integral is free of ultraviolet and infrared divergences as we approach Minkowski space (ω=2). It is also shown that the ultraviolet divergences arising from two‐loop massless tadpole integrals either vanish completely as ω→2, or manifest themselves as poles of Weierstrass' gamma function.

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