On the Uncertainty Principle for Metaplectic Transformations

TL;DR

This paper extends the Heisenberg Uncertainty Principle to operators within the Metaplectic group across any dimension, providing new proofs and generalizations of existing uncertainty principles.

Contribution

It offers a novel proof of the Uncertainty Principle for Metaplectic operators in arbitrary dimensions, expanding the theoretical framework of quantum mechanics and harmonic analysis.

Findings

Proof of the Uncertainty Principle for Metaplectic operators in any dimension

Extension of previous uncertainty principles to a broader class of operators

New theoretical insights into the structure of the Metaplectic group

Abstract

We explore the new proofs and extensions of the Heisenberg Uncertainty Principle introduced by A.~Widgerson & Y.~Widgerson in [MR4229152], developed in [MR4453622] by N.C.~Dias, F.~Luef and J.N.~Prata and also in [MR4337266] by Y.~Tang. In particular we give here a proof of the Uncertainty Principle for operators in the Metaplectic group in any dimension.