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MiS Preprint

A Note on the Square of Dirac Type Differential Operators

Jürgen Tolksdorf


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.

MSC Codes:
53C05, 53C07
02.40.Hw, 02.40.Ma
Clifford Module Bundles, Dirac Type Differential Operators, Linear Connections

Related publications

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