We present a comprehensive survey of the dynamics of spin-polarized beams in high-energy particle accelerators. A major theme of this review is to clarify the distinction between the properties of an individual particle—a spin—and that of a beam—the polarization. We include work from a number of institutions, including high- and medium-energy facilities, synchrotron light sources and muon storage rings (including a proposal to measure the muon electric dipole moment) and, briefly, linear accelerators and recirculating linacs. High-precision tests of the Standard Model using spin-polarized beams are reviewed; also innovative studies using spin dynamics as a tool for accelerator physics per se. We include important historical works as well as modern developments in the field. The fundamental theory is derived in detail, starting from the basic principles of quantum mechanics, electrodynamics and statistical mechanics, as well as 'accelerator physics'. The principal theoretical formulae in the field (Froissart–Stora, Sokolov–Ternov and Derbenev–Kondratenko) are presented, with in-depth attention to the quantum-statistical mechanics, as opposed to purely 'accelerator physics'.

Publisher's note. A related review article by the same authors, Siberian Snakes in high-energy accelerators, has been published in Journal of Physics G: Nuclear and Particle Physics, volume 31, page R151