A Few Almost Trivial Notes on the Symplectic Radon Transform and the Tomographic Picture of Quantum Mechanics

TL;DR

This paper explores the symplectic Radon transform and its role in quantum mechanics, highlighting the importance of the metaplectic group and quadratic Fourier transforms for better understanding and applications.

Contribution

It introduces a pedagogical perspective connecting the Radon transform with the metaplectic group and quadratic Fourier transforms, enhancing understanding in quantum mechanics and time-frequency analysis.

Findings

Clarifies the role of the metaplectic group in the Radon transform

Links quadratic Fourier transforms to symplectic geometry

Provides educational insights for researchers in related fields

Abstract

We emphasize in these pedagogical notes the that the theory of the Radon transform and its applications is best understood using the theory of the metaplectic group and the quadratic Fourier transforms generating metaplectic operator.. Doing this we hope that these notes will be useful to a larger audience, including researchers in time-frequency analysis.