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29 March 2024
 
  » arxiv » 1301.2652

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Noncommutative Residue and Dirac operators for Manifolds with the Conformal Robertson-Walker metric
Jian Wang ; Yong Wang ;
Date 12 Jan 2013
AbstractIn this paper, we prove a Kastler-Kalau-Walze type theorem for 4-dimensional and 6-dimensional spin manifolds with boundary associated with the conformal Robertson-Walker metric. And we give two kinds of operator theoretic explanations of the gravitational action for boundary in the case of 4-dimensional manifolds with flat boundary. In particular, for 6-dimensional spin manifolds with boundary with the conformal Robertson-Walker metric, we obtain the noncommutative residue of the composition of $pi^+D^{-1}$ and $pi^+D^{-3}$ is proportional to the Einstein-Hilbert action for manifolds with boundary.
Source arXiv, 1301.2652
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