Geometric Representation of Generalized Coherent States and their Symplectic Capacities: A Synthetic Approach

In this work we review, complete, and synthesize results linking generalized coherent stages (nondegradable Gaussian wavefunctions) to the notions of Fermi ellipsoids, quantum blobs, and microlocal pairs introduced in previous work. These geometric objects are Fermi ellipsoids, quantum blobs, and microlocal pairs. In addition we study various symplectic capacities associated with these objects.