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Topological obstructions to the diagonalisation of pseudodifferential systems
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Topological obstructions to the diagonalisation of pseudodifferential systems

Matteo Capoferri, Grigori Rozenblum, Nikolai Saveliev and Dmitri Vassiliev
arXiv.org, Vol.9(43), pp.472-486
Cornell University Library, arXiv.org
2022-12-27
DOI: https://doi.org/10.1090/bproc/147

Abstract

Eigenvectors Obstructions Operators (mathematics) Topology
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.
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https://doi.org/10.1090/bproc/147View
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