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arXiv · 2511.18549

Non-Symplectic Deformations of Geometric Quantisation

Kerr Maxwell
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Abstract

We introduce the notion of geometric pseudo-quantisation based on geometric quantisation with a weakened curvature condition. We show how such a structure arises naturally from simple deformations of the symplectic structure and pullbacks of prequantum data by non-symplectic diffeomorphisms. Our main result is deriving the equations of motion for some simple pseudo-quantisations. We also compute the pseudo-quantisation of several simple examples from symplectic and almost-symplectic geometry, as well as the general form of the resulting deformed canonical commutator.

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Kerr Maxwell. 2025-11-23. Non-Symplectic Deformations of Geometric Quantisation. https://arxiv.org/abs/2511.18549

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