Principles of Invariance in Radiative Transfer

We have reviewed the principle of invariance, its applications and its usefulness for obtaining the radiation field in semi-infinite and finite atmospheres. Various laws of scattering in dispersive media and the consequent radiation field are studied. The H-functions and X- and Y-functions in semi-infinite and finite media respectively are derived in a few cases. The Discrete Space Theory (DST) which is a general form of the Principle of Invariance is described. The method of addition of layers with general properties, is shown to describe all the properties of multiple scattering. A few examples of the application of DST such as polarization, line formation in expanding stellar atmospheres, etc., and a numerical analysis of DST are presented. Other developments in the theory of radiative transfer are briefly described. This revised version was published online in June 2006 with corrections to the Cover Date.