On the geometry of $Diff(S^1)-$pseudodifferential operators based on renormalized traces
Differential Geometry
2020-07-02 v1 High Energy Physics - Theory
Mathematical Physics
math.MP
Operator Algebras
Abstract
In this article, we examine the geometry of a group of Fourier-integral operators, which is the central extension of with a group of classical pseudo-differential operators of any order. Several subgroups are considered, and the corresponding groups with formal pseudodifferential operators are defined. We investigate the relationship of this group with the restricted general linear group we define a right-invariant pseudo-Riemannian metric on it that extends the Hilbert-Schmidt Riemannian metric by the use of renormalized traces of pseudo-differential operators, and we describe classes of remarkable connections.
Cite
@article{arxiv.2007.00387,
title = {On the geometry of $Diff(S^1)-$pseudodifferential operators based on renormalized traces},
author = {Jean-Pierre Magnot},
journal= {arXiv preprint arXiv:2007.00387},
year = {2020}
}