Some remarks on open quantum systems

The spin–boson model is the simplest non-exactly solvable model describing the interaction of matter with radiation. I will review the historical development of this model, beginning with Einstein’s 1917 derivation of Planck’s law from detailed balance between emission and absorption of radiation, and Dirac’s 1927 paper “The Quantum Theory of the Emission and Absorption of Radiation.” The Araki–Woods representation of the canonical commutation relations, introduced in 1963, has its roots in these early works and lies at the heart of modern developments in the study of the spin–boson model. I will explain its role in these developments and discuss some open problems.