Statistics of the Thermal Radiation Field

Abstract

The characteristic functional is calculated for a system of bosons obeying linear field equations. The system is assumed to be in equilibrium, and the density matrix is taken to be of the form $〈\mathrm{}\left\{n\right\}\left|\rho \mathrm{}\right|\left\{m\right\}\mathrm{}〉=\Pi {\kappa }^{}\left[{\delta }_{n_{\kappa }{m}_{\kappa }}\right(1-z_{\kappa }\left){z_{\kappa }}^{n_{\kappa }}\right]$, where $\kappa$ labels the individual modes. From the characteristic functional, the moments and distribution functions of an arbitrary number of field components are derived. In addition, it is shown how to obtain the density matrix from the characteristic functional, and, for the system in question, the original density matrix is recovered. Explicit calculations are performed for the electromagnetic field in an unbounded domain and in a semi-infinite domain bounded by a perfectly conducting plane.