Graphical Representation of Invariants and Covariants in General Relativity

Abstract

We present a grapical way to describe invariants and covariants in the (4 dim) general relativity. This makes us free from the complexity of suffixes . Two new off-shell relations between (mass)$\ast \ast 6$\ invariants are obtained. These are important for 2-loop off-shell calculation in the perturbative quantum gravity. We list up all independent invarians with dimensions of (mass)$\ast \ast 4$\ and (mass)$\ast \ast 6$. Furthermore the explicit form of 6 dim Gauss-Bonnet identity is obtained.

27 pages

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