A note on the Einstein-Hilbert action and Dirac operators on R~n

摘要

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 W. The result is then obtained by using the properties of heat kernels and generalised Laplacians.