On diffeological principal bundles of non-formal pseudo-differential operators over formal ones

TL;DR

This paper explores the structure of diffeological bundles of non-formal pseudo-differential operators over formal ones, focusing on their structure groups and the properties of diffeological principal bundles without assuming local trivializations.

Contribution

It introduces new insights into the structure of diffeological principal bundles of pseudo-differential operators, leveraging smoothing connections and addressing open questions.

Findings

Characterization of the bundle structure of pseudo-differential operators

Analysis of the structure group in the diffeological setting

Discussion of open problems in the theory of diffeological bundles

Abstract

We describe the structure of diffeological bundle of non formal classical pseudo-differential operators over formal ones, and its structure group. For this, we give few results on diffeological principal bundles with (a priori) no local trivialization, use the smoothing connections alrealy exhibited by the author in previous works, and finish with open questions.