Symplectic Radon Transform and the Metaplectic Representation

We study the symplectic Radon transform from the point of view of the metaplectic representation of the symplectic group and its action on the Lagrangian Grassmannian. We give rigorous proofs in the general setting of multi-dimensional quantum systems. We interpret the inverse Radon transform as a “demarginalization process” for the Wigner distribution. This work completes, by giving complete proofs, a previous Note.