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

TL;DR

This paper reviews and synthesizes geometric representations of generalized coherent states, exploring their connections to Fermi ellipsoids, quantum blobs, and symplectic capacities within a unified framework.

Contribution

It provides a comprehensive synthesis of geometric and symplectic aspects of generalized coherent states, extending previous results and exploring new symplectic capacities.

Findings

Unified geometric framework for coherent states and related objects

Connections between Fermi ellipsoids, quantum blobs, and microlocal pairs

Analysis of symplectic capacities associated with these geometric objects

Abstract

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.