@misc{MickelssonPaycha2011,
author = {Mickelsson, Jouko and Paycha, Sylvie},
title = {The logarithmic residue density of a generalized Laplacian},
series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
journal = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
number = {649},
issn = {1866-8372},
doi = {10.25932/publishup-41368},
url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-413680},
pages = {28},
year = {2011},
abstract = {We show that the residue density of the logarithm of a generalized Laplacian on a closed manifold defines an invariant polynomial-valued differential form. We express it in terms of a finite sum of residues of classical pseudodifferential symbols. In the case of the square of a Dirac operator, these formulas provide a pedestrian proof of the Atiyah-Singer formula for a pure Dirac operator in four dimensions and for a twisted Dirac operator on a flat space of any dimension. These correspond to special cases of a more general formula by Scott and Zagier. In our approach, which is of perturbative nature, we use either a Campbell-Hausdorff formula derived by Okikiolu or a noncommutative Taylor-type formula.},
language = {en}
}
@article{MickelssonPaycha2010,
author = {Mickelsson, Jouko and Paycha, Sylvie},
title = {The logarithmic residue density of a generalized Laplacian},
series = {Journal of the Australian Mathematical Society},
volume = {90},
journal = {Journal of the Australian Mathematical Society},
number = {1},
publisher = {Cambridge Univ. Press},
address = {Cambridge},
issn = {0263-6115},
doi = {10.1017/S144678871100108X},
pages = {53 -- 80},
year = {2010},
abstract = {We show that the residue density of the logarithm of a generalized Laplacian on a closed manifold definesan invariant polynomial-valued differential form. We express it in terms of a finite sum of residues ofclassical pseudodifferential symbols. In the case of the square of a Dirac operator, these formulas providea pedestrian proof of the Atiyah-Singer formula for a pure Dirac operator in four dimensions and for atwisted Dirac operator on a flat space of any dimension. These correspond to special cases of a moregeneral formula by Scott and Zagier. In our approach, which is of perturbative nature, we use either aCampbell-Hausdorff formula derived by Okikiolu or a noncommutative Taylor-type formula.},
language = {en}
}