A Canonical Trace Associated with Certain Spectral Triples

TL;DR

This paper derives a general formula for discrepancies in zeta-regularized traces within the spectral triples framework and introduces a canonical trace for operators outside the dimension spectrum.

Contribution

It provides a new formula for trace discrepancies and defines a canonical trace for operators outside the spectral triple's dimension spectrum.

Findings

Derived a general formula for zeta-regularized trace discrepancies

Introduced a canonical trace for operators outside the dimension spectrum

Enhanced understanding of spectral triples and trace theory

Abstract

In the abstract pseudodifferential setup of Connes and Moscovici, we prove a general formula for the discrepancies of zeta-regularised traces associated with certain spectral triples, and we introduce a canonical trace on operators, whose order lies outside (minus) the dimension spectrum of the spectral triple.