Title: Quantum Harmonic Analysis of the Density Matrix: Basics,
Abstract: In this Review we will study rigorously the notion of mixed states and their
density matrices. We mostly give complete proofs. We will also discuss the
quantum-mechanical consequences of possible variations of Planck's constant h.
This Review has been written having in mind two readerships: mathematical
physicists and quantum physicists. The mathematical rigor is maximal, but the
language and notation we use throughout should be familiar to physicists.