Bosonic Pairings

TL;DR

This paper extends the inner product concept in bosonic Fock space to a pairing between antifunctionals, with applications in geometric quantization.

Contribution

It introduces a new pairing framework for antifunctionals on the symmetric algebra, generalizing the inner product in bosonic Fock space.

Findings

Established a pairing between antifunctionals on symmetric algebra.

Illustrated the pairing with Gaussian half-form pairing in geometric quantization.

Extended the mathematical tools for bosonic Fock space analysis.

Abstract

We extend the inner product from bosonic Fock space to a pairing between suitable antifunctionals on the symmetric algebra. Our account is illustrated by the (Gaussian) half-form pairing between positive polarizations in the form needed for geometric quantization.