On the thermodynamics of quantum-electrodynamic frequency shifts

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Abstract
The spectra of atoms exposed to black-body radiation suffer temperature-dependent frequency shifts predicted earlier and now becoming measurable, whose thermodynamic status is clarified. To a good approximation, they are calculable as differences between the coupling-induced shifts in the Helmholtz free energies of the coupled system atom plus quantised electromagnetic field, in thermal equilibrium subject to the constraint that the atom is in a given state li). Effectively, the state label i plays the same role as do macroscopically controlled variables in ordinary thermodynamics. With kT well below the electron rest-mass energy, such calculations require only the forward scattering amplitude of light from the atom; some previously overlooked but theoretically interesting relativistic features of the exact expressions are pointed out. For a harmonic oscillator, uniquely, the constrained free-energy shift is the same for all levels (and therefore also the same as the shift in unconstrained equilibrium); consequently there is no thermal frequency shift at all. Recent comments on black-body-induced Stark shifts by Ford et al. (1985-6) are based on their calculation of the free energy of a harmonic oscillator in unconstrained equilibrium with the field. It is shown that as regards frequency shifts their comments are incompatible with, and misrepresent, previous correct work on such shifts.