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

作者：Battisti Ubertino^*; Coriasco Sandro

来源：Journal of Pseudo-Differential Operators and Applications, 2011, 2(3): 303-315.

DOI：10.1007/s11868-011-0031-8

• Wodzicki residue
• Einstein-Hilbert action
• Dirac operator

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.

• 出版日期2011-9