Matteo Capoferri, G. Rozenblum, N. Saveliev, D. Vassiliev
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Topological obstructions to the diagonalisation of pseudodifferential systems
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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