The metaplectic correction in geometric quantization

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 $P$ be a polarization on a symplectic manifold for which there exists a metalinear frame bundle. We show that for any other compatible polarization $P'$ 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 $P$) to achieve this goal, and thus the name "metaplectic correction" is inappropriate.