A Note on the Einstein-Hilbert action and the Dirac operator on R^n
Functional Analysis
2013-09-05 v2 Operator Algebras
Abstract
We prove an extension to R^n, endowed with a suitable metric, of the relation between the Einstein-Hilbert action and the Dirac operator which holds on closed spin manifolds. By means of complex powers, we first define the regularised Wodzicki Residue for a class of operators globally defined on R^n. The result is then obtained by using the properties of heat kernels and generalised Laplacians.
Keywords
Cite
@article{arxiv.1007.1797,
title = {A Note on the Einstein-Hilbert action and the Dirac operator on R^n},
author = {U. Battisti and S. Coriasco},
journal= {arXiv preprint arXiv:1007.1797},
year = {2013}
}
Comments
10 pages, 1 figure. Corrected typos; expanded references and section 1; slightly modified figure, abstract, introduction and some notation; material of section 3 reorganised, according to changes in previous sections