Topological obstructions to the diagonalisation of pseudodifferential systems
Analysis of PDEs
2023-01-02 v3 Mathematical Physics
math.MP
Abstract
Given a matrix pseudodifferential operator on a smooth manifold, one may be interested in diagonalising it by choosing eigenvectors of its principal symbol in a smooth manner. We show that diagonalisation is not always possible, on the whole cotangent bundle or even in a single fibre. We identify global and local topological obstructions to diagonalisation and examine physically meaningful examples demonstrating that all possible scenarios can occur.
Keywords
Cite
@article{arxiv.2203.16957,
title = {Topological obstructions to the diagonalisation of pseudodifferential systems},
author = {Matteo Capoferri and Grigori Rozenblum and Nikolai Saveliev and Dmitri Vassiliev},
journal= {arXiv preprint arXiv:2203.16957},
year = {2023}
}
Comments
v3: final version