Phys. Rev. D 35, 769–770 (1987)Two important invariant identitiesReceived 23 June 1986; published in the issue dated 15 January 1987 Two important invariant identities about the products of the Riemann tensor Rαβγλ and the Ricci tensor Rαβ and the scalar curvature R are derived by the technique of Weyl decomposition of the Riemann tensor and by the spinor formalism. These identities are very useful in four dimensions for simplifying the final expression of the a3 coefficient of the scalar fields and for simplifying the evaluation of the vacuum-polarization energy-momentum tensor. This result is of relevance to the work of Jack and Parker on the summed form of the heat kernel. © 1987 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevD.35.769
DOI:
10.1103/PhysRevD.35.769
PACS:
04.60.+n, 02.40.+m, 04.20.Cv, 11.10.Gh
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