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arXiv · 2608.22443

A Differential Characterization of the Metaplectic Kernel

Benjamin Cahen
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Abstract

We present a derivation of the integral kernel of a metaplectic representation operator in the Bargmann-Fock model based solely on its defining intertwining property with the Heisenberg representation. Expressing a metaplectic operator as an integral operator transforms the corresponding infinitesimal intertwining identities into a system of first-order partial differential equations satisfied by its kernel. We show that this system determines the kernel (up to a unit scalar) which is precisely the classical Gaussian associated with the symplectic transformation. A similar result is obtained for the Schr\"odinger model.

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Benjamin Cahen. 2026-08-23. A Differential Characterization of the Metaplectic Kernel. https://arxiv.org/abs/2608.22443

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