The metaplectic correction in geometric quantization
Gijs M. Tuynman

TL;DR
This paper demonstrates that the so-called 'metaplectic correction' in geometric quantization can be achieved without the metaplectic frame bundle, by establishing a unique metalinear frame bundle for compatible polarizations.
Contribution
It shows that the traditional reliance on the metaplectic frame bundle is unnecessary, providing a new perspective on geometric quantization.
Findings
Existence of a unique metalinear frame bundle for compatible polarizations.
The BKS-pairing can be well defined without the metaplectic frame bundle.
The term 'metaplectic correction' is considered inappropriate in this context.
Abstract
Let be a polarization on a symplectic manifold for which there exists a metalinear frame bundle. We show that for any other compatible polarization there exists a unique metalinear frame bundle such that the BKS-pairing is well defined. This means that we do not need the metaplectic frame bundle (nor a positivity condition on ) to achieve this goal, and thus the name "metaplectic correction" is inappropriate.
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