Quantum electrodynamics in the presence of dielectrics and conductors. V. The extinction and moment theorems for correlation functions and relativistic aspects of blackbody fluctuations

Abstract

Dynamical laws describing the space-time development of the response functions and second-order correlation functions of the electromagnetic fields in a linear dielectric medium are presented in the form of a number of differential and integral equations. The boundary conditions on the response functions are expressed as extinction theorems, which are particularly useful for systems involving rough surfaces and metallic gratings. Higher-order correlation functions are shown to be related to the linear-response functions in a manner analogous to the moment theorem for Gaussian random processes. A modified form of the fluctuation-dissipation theorem is obtained and is used to calculate free-space blackbody fluctuations in a moving frame. Fluctuations in a moving dielectric are obtained from the transformation of fields under Lorentz transformation. Contact with the earlier works of Mehta and Wolf, Eberly and Kujawski, and the recent work of Baltes and co-workers on blackbody radiation is made wherever possible. Finally, the correlation functions in a moving frame are used to discuss the relaxation of a moving atom. The discussion in the last section is for the case of free space.