(Second) Quantised resolvents and regularised traces
type: Item
instance of: scholarly article
title: (Second) Quantised resolvents and regularised traces
zbMATH Open document ID: 1118.58015
author: Sylvie Paycha
published in: Journal of Geometry and Physics
publication date: 2007-04-27T00:00:00Z
review text: Let \(Q\) be a classical elliptic pseudodifferential operator acting on smooth sections of a vector bundle \(E\) over a close manifold \(M\). It is showed that if \(Q\) has scalar leading symbol then quantised weighted traces \(\text{ tr}_n^{Q+\theta}\) can be expressed as a finite linear combination of noncommutative residues, thus the traces are local for any positive integer \(n\). Moreover, when \(Q\) has positive leading symbol then heat-kernel quantised weighted traces coincide for large quantum level with the quantised weighted traces. This contrasts with a zero level. As a consequence it is show that the anomaly of a quantised regular trace of level \(n\) is a finite linear combination of quantised regularised traces of level \(n+1\). In particular, if \(Q\) has scalar leading symbol then their Hochschild coboundary is also local as a finite linear combination of noncommutative residues. Moreover, the local expressions for the variation of quantised weighted traces and the exterior differential of quantised reqularised traces are proved.
reviewed by: Leszek Skrzypczak
Mathematics Subject Classification ID: 58J42
Mathematics Subject Classification ID: 58J40
zbMATH DE Number: 5147163
zbMATH Keywords: traces
zbMATH Keywords: pseudodifferential operators
zbMATH Keywords: noncommutative residue
MaRDI profile type: Publication
full work available at URL: j.geomphys.2006.10.010
OpenAlex ID: W2083854122
cites work: RENORMALIZED LAPLACIANS ON A CLASS OF HILBERT MANIFOLDS AND A BOCHNER–WEITZENBÖCK TYPE FORMULA FOR CURRENT GROUPS
cites work: The Atiyah-Singer index theorem for families of Dirac operators: Two heat equation proofs
cites work: Q4451321
cites work: The analysis of elliptic families. I: Metrics and connections on determinant bundles
cites work: From tracial anomalies to anomalies in quantum field theory
cites work: WEIGHTED TRACES ON ALGEBRAS OF PSEUDO-DIFFERENTIAL OPERATORS AND GEOMETRY ON LOOP GROUPS
cites work: The local index formula in noncommutative geometry
cites work: Q4888825
cites work: Q4668561
cites work: On the Logarithm Component in Trace Defect Formulas
cites work: Q3593685
cites work: Weakly parametric pseudodifferential operators and Atiyah-Patodi-Singer boundary problems
cites work: A new proof of Weyl's formula on the asymptotic distribution of eigenvalues
cites work: Q3437619
cites work: Fourier integral operators. I
cites work: Quantum K-theory. I: The Chern character
cites work: Q4872763
cites work: On the noncommutative residue for pseudodifferential operators with log-polyhomogeneous symbols
cites work: Anomalies and Schwinger terms in NCG field theory models
cites work: Fractional analytic index
cites work: Renormalised Chern-Weil forms associated with families of Dirac operators
cites work: RENORMALIZED TRACES AS A LOOKING GLASS INTO INFINITE-DIMENSIONAL GEOMETRY
cites work: Q3593681
cites work: A Laurent expansion for regularized integrals of holomorphic symbols
cites work: Q5542418
cites work: Q4725211
DOI: 10.1016/J.GEOMPHYS.2006.10.010
description: scientific article; zbMATH DE number 5147163