A Note on the Einstein-Hilbert action and the Dirac operator on R^n
arXiv:1007.1797 · doi:10.1007/s11868-011-0031-8
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. 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.
10 pages, 1 figure. Corrected typos; expanded references and section 1; slightly modified figure, abstract, introduction and some notation; material of section 3 reorganised, according to changes in previous sections
References in corpus (5)
- Differential Forms and the Wodzicki Residue for Manifolds with Boundary
- Differential Forms and the Noncommutative Residue for Manifolds with Boundary in the Non-product Case
- Noncommutative geometry and lower dimensional volumes in Riemannian geometry
- Wodzicki Residue for Operators on Manifolds with Cylindrical Ends
- Spectral Bounds for Dirac Operators on Open Manifolds