Diagrammatic derivation of Lovelock densities

C. Bogdanos
Phys. Rev. D 79, 107501 – Published 21 May 2009

Abstract

We discuss a method of calculating the various scalar densities encountered in Lovelock theory, which relies on diagrammatic, instead of algebraic manipulations. Taking advantage of the known symmetric and antisymmetric properties of the Riemann tensor that appears in the Lovelock densities, we map every quadratic or higher contraction into a corresponding permutation diagram. The derivation of the explicit form of each density is then reduced to identifying the distinct diagrams, from which we can also read off the overall combinatoric factors. The method is applied to the first Lovelock densities, of order two (Gauss-Bonnet term) and three.

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  • Received 19 April 2009

DOI:https://doi.org/10.1103/PhysRevD.79.107501

©2009 American Physical Society

Authors & Affiliations

C. Bogdanos*

  • Laboratoire de Physique Theorique, Université de Paris-Sud 11, Bâtiment 210, 91405 Orsay CEDEX, France

  • *Charalampos.Bogdanos@th.u-psud.fr

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Issue

Vol. 79, Iss. 10 — 15 May 2009

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