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. We give first a direct proof of the result on R^4. Then, by means of complex powers and a regularised Wodzicki Residue for a class of operators globally defined on R^n, we show a similar result for n>=4 by using the properties of heat kernels and Dirac operators.

A Note on the Einstein-Hilbert Action and the Dirac Operator on R^n

BATTISTI, UBERTINO;CORIASCO, Sandro
2011

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. We give first a direct proof of the result on R^4. Then, by means of complex powers and a regularised Wodzicki Residue for a class of operators globally defined on R^n, we show a similar result for n>=4 by using the properties of heat kernels and Dirac operators.
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http://arxiv.org/pdf/1007.1797v2
http://www.springer.com/birkhauser/mathematics/journal/11868
Wodzicki Residue; Einstein-Hilbert action; Dirac operator.
Ubertino Battisti; Sandro Coriasco
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/90727
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