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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
90/2006

A Note on the Square of Dirac Type Differential Operators

Jürgen Tolksdorf

Abstract

The aim of this note is to present a new global formula for the Lichnerowicz decomposition of a general Dirac type first order differential operator. This formula generalizes the well-known Lichnerowicz formula for Dirac type operators which are determined by Clifford connections on an arbitrary Clifford module bundle.

Moreover, we also show that the connection class of a general Dirac type operator has a natural representative. In this sense, each Dirac type operator defines a natural connection on a given Clifford module bundle. This generalizes the fact that the connection class of a Dirac type operator possesses at most one Clifford connection.

Received:
Aug 24, 2006
Published:
Aug 24, 2006
MSC Codes:
53C05, 53C07
PACS:
02.40.Hw, 02.40.Ma
Keywords:
Clifford Module Bundles, Dirac Type Differential Operators, Linear Connections

Related publications

inJournal
2007 Repository Open Access
Jürgen Tolksdorf

On the square of first order differential operators of Dirac type and the Einstein-Hilbert action

In: Journal of geometry and physics, 57 (2007) 10, pp. 1999-2013