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A note on the Einstein–Hilbert action and Dirac operators on \({\mathbb{R}^n}\)

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Abstract

We prove an extension to \({\mathbb{R}^n}\), 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 \({\mathbb{R}^n}\). The result is then obtained by using the properties of heat kernels and generalised Laplacians.

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  1. Dipartimento di Matematica, Università di Torino, Turin, Italy

    Ubertino Battisti & Sandro Coriasco

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  1. Ubertino Battisti
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  2. Sandro Coriasco
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Correspondence to Ubertino Battisti.

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Battisti, U., Coriasco, S. A note on the Einstein–Hilbert action and Dirac operators on \({\mathbb{R}^n}\) . J. Pseudo-Differ. Oper. Appl. 2, 303–315 (2011). https://doi.org/10.1007/s11868-011-0031-8

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  • DOI: https://doi.org/10.1007/s11868-011-0031-8

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