All about displacements

The general idea of this paper consists in construction of the coherent states by means of gauge-invariant operators of finite displacements (GID). Their properties are discussed and next the applications to various physical phenomena (Planck thermal averaging, vacuum polarization, magnetic properties of the electron gas, Landau diamagnetism, de Haas-van Alphen oscillations, quantum Hall effect and properties of possible “q-particles”) are presented. The connection with quantum algebras is considered on the base of Bogoliubov-like transformation of GIDʹs. This connection may be used for explicit construction of irreps of q-algebras.