## 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.

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.

Original language | English |
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Pages (from-to) | 472-486 |

Number of pages | 15 |

Journal | Proceedings of the American Mathematical Society: Series B |

Volume | 9 |

Issue number | 43 |

DOIs | |

Publication status | Published - 27 Dec 2022 |

## Keywords

- math.AP
- math-ph
- math.MP
- primary 58J40, secondary 35G35, 35J46, 35J47, 35J48

## ASJC Scopus subject areas

- Analysis
- Discrete Mathematics and Combinatorics
- Geometry and Topology
- Algebra and Number Theory