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Dominique Manchon and Sylvie Paycha - uni-potsdamde.pdf
Dominique Manchon and Sylvie Paycha - uni-potsdamde
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10.1.1.142.7188 - Renormalised Chern-Weil Forms Associated with Families of Dirac operators (2006) by Jouko Mickelsson , Sylvie Paycha.pdf
We provide local expressions for Chern-Weil type forms built from uperconnections associated with families of Dirac perators previously investigated in [Sc] and later in [PS1]. When the underlying fibration of manifolds is trivial, the even degree orms can be interpreted as renormalised Chern-Weil forms in as far as they coincide with regularised Chern-Weil forms up to residue correction terms. Similarly, a new formula for the curvature of the local fermionic vacuum line bundles is derived using a residue correction term added to the naive curvature formula. We interpret the odd degree Chern-Weil type forms built from superconnections as Wodzicki residues and establish a transgression formula along the lines of known transgression formulae for η-forms.
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