Infrared divergences, radiative corrections, and bremsstrahlung in the presence of a thermal-equilibrium radiation background

The theory of infrared radiative corrections is generalized to include a blackbody radiation background. Although ${\omega }^{\mathrm{-}2}$ divergences appear now, proper inclusion of stimulated transitions in both the virtual- and real-photon contributions leads to the elimination of all divergences, and yields a temperature-dependent asymmetric energy-loss spectrum which is flat in the origin. This spectrum is the convolution of the known spontaneous-emission spectrum with an analytic spectrum describing stimulated transitions, and is calculated explicitly. Thus, 1/f noise is background invariant.