Affiliation:
1. Department of Physics, University of Shizuoka, Yada 52-1, Shizuoka 422-8526, Japan
2. Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-01, Japan
Abstract
We present some approaches to the perturbative analysis of the classical and quantum gravity. First we introduce a graphical representation for a global SO (n) tensor (∂)dhαβ, which generally appears in the weak field expansion around the flat space: gμν=δμν+hμν. Making use of this representation, we explain (1) Generating function of graphs (Feynman diagram approach), (2) Adjacency matrix (Matrix approach), (3) Graphical classification in terms of "topology indices" (Topology approach), (4) The Young tableau (Symmetric group approach). We systematically construct the global SO (n) invariants. How to show the independence and completeness of those invariants is the main theme. We explain it taking simple examples of ∂∂h-, and (∂∂h)2-invariants in the text. The results are applied to the analysis of the independence of general invariants and (the leading order of) the Weyl anomalies of scalar-gravity theories in "diverse" dimensions (2,4,6,8,10 dimensions).
Publisher
World Scientific Pub Co Pte Lt
Subject
Astronomy and Astrophysics,Nuclear and High Energy Physics,Atomic and Molecular Physics, and Optics