A generalized Lichnerowicz formula, the Wodzicki Residue and Gravity

Ackermann, Thomas ; Tolksdorf, Jürgen

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URL: https://ub-madoc.bib.uni-mannheim.de/1651
URN: urn:nbn:de:bsz:180-madoc-16518
Document Type: Working paper
Year of publication: 1994
The title of a journal, publication series: None
Publication language: English
Institution: School of Business Informatics and Mathematics > Sonstige - Fakultät für Wirtschaftsinformatik und Wirtschaftsmathematik
Subject: 510 Mathematics
Subject headings (SWD): Nichtkommutative Differentialgeometrie , Lichnerowicz, André , Dirac-Operator , Wärmeleitungskern , Schwere
Keywords (English): non-commutative geometry , Lichnerowicz formula , Dirac operator , heat-kernel-expansion , Wodzicki residue , gravity
Abstract: We prove a generalized version of the well-known Lichnerowicz formula for the square of_the most general Dirac operator ∼D on an even-dimensional spin manifold associated to a metric connection ∼∇. We use thiS formula to compute the subleading term φ1(x,x,∼D2) of the heat-kernel expansion of ∼D2. The trace of this term plays a key-rôle in the definition of a (euclidian) gravity action in the context of non-commutative geometry. We show that thhis gravity action can be interpreted as defining a modified euclidian Einstein-Cartan theory.
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