ABSTRACT
The statistical study of a system of bosons has a peculiar status in the history of physics: it is for describing what would nowadays be called a gas of photons that Planck introduced the first quantum hypothesis in 1900. The first part of this chapter is devoted to the statistical analysis of a system of bosons of zero chemical potential, corresponding to the elementary excitations of a given system, as those initially studied by Planck (Sections 7.1, 7.2 and 7.3). The canonical and grand canonical point of views are strictly equivalent when dealing with such quanta of excitation (see Section 7.1.2). This is no longer the case when the number of particles is conserved, and is associated to the phenomenon of Bose–Einstein condensation which is studied in Section 7.4.
