A Pseudodifferential Analytic Perspective on Getzler's Rescaling
Résumé
Inspired by Gilkey's invariance theory, Getzler's rescaling method and
Scott's
approach to the index via Wodzicki residues, we give a localisation
formula for the
$\mathbb Z_2$-graded Wodzicki residue of the logarithm of a class of
differential operators
acting on sections of a spinor bundle over an even-dimensional manifold.
This formula is
expressed in terms of another local density built from the symbol of the
logarithm of
a limit of rescaled differential operators acting on differential forms.
When applied
to complex powers of the square of a Dirac operator, it amounts to
expressing the index
of a Dirac operator in terms of a local density involving the logarithm
of the Getzler
rescaled limit of its square.
Domaines
Géométrie différentielle [math.DG]
Origine : Fichiers produits par l'(les) auteur(s)