A Note on the Einstein-Hilbert action and the Dirac operator on R^n

Details A Note on the Einstein-Hilbert action and the Dirac operator on R^n A Note on the Einstein-Hilbert action and the Dirac operator on R^n

2010-07-11

arxiv.org/abs/1007.1797v2

Mathematics

Functional Analysis

10 pages, 1 figure. Corrected typos; expanded references and section 1; slightly modified figure, abstract, introduction and s

Scientific paper

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.

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