Square integrable representations, an invaluable tool

Abstract

Square integrable representations are not only remarkable objects in abstract harmonic analysis, but also an invaluable tool in various fields of theoretical physics and applied mathematics. We will focus on the role that they play in the definition of coherent states, in wavelet analysis, in the phase-space formulation of quantum mechanics and in the associated star product formalism, and in some applications related to quantum dynamical semigroups.