Renormalised Chern-Weil forms associated with families of Dirac operators
2007 (English)In: Journal of Geometry and Physics, ISSN 0393-0440, Vol. 57, no 9, 1789-1814 p.Article in journal (Refereed) Published
We provide local expressions for Chern-Weil type forms built from superconnections associated with families of Dirac operators previously investigated in [S. Scott, Zeta-Chern forms and the local family index theorem, Trans. Amer. Math. Soc. (in press). arXiv: math.DG/0406294] and later in [S. Paycha, S. Scott, Chern-Weil forms associated with superconnections, in: B. Booss-Bavnbeck, S. Klimek, M. Lesch, W. Zhang (Eds.), Analysis, Geometry and Topology of Elliptic Operators, World Scientific, 2006]. When the underlying fibration of manifolds is trivial, the even degree forms 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 eta-forms.
Place, publisher, year, edition, pages
2007. Vol. 57, no 9, 1789-1814 p.
chem character, infinite rank vector bundles, index theorems for Dirac type operators, renormalised traces, residues of pseudodifferential operators, gerbes, infinite dimensional Grassmann manifolds
IdentifiersURN: urn:nbn:se:kth:diva-37079DOI: 10.1016/j.geomphys.2007.03.001ISI: 000247504100004ScopusID: 2-s2.0-34248998246OAI: oai:DiVA.org:kth-37079DiVA: diva2:432012