Thermal QED theory for bound states

Abstract

This paper presents the Quantum Electrodynamics theory for bound states at finite temperatures. To describe the thermal effects arising in a heat bath, the Hadamard form of a thermal photon propagator is employed. As the form allows a simple introduction of thermal gauges in a way similar to the ‘ordinary’ Feynman propagator, the gauge invariance can be proved for all of the considered effects. Moreover, unlike the ‘standard’ form of the thermal photon propagator, the Hadamard expression offers well-defined analytical properties, yet contains a divergent contribution, which requires the introduction of a regularization procedure within the framework of the constructed theory. The method and physical interpretation of regularization are given in the paper. Correctness of the procedure is confirmed also by the gauge invariance of final results and the coincidence of the results (as exemplified by the self-energy correction) for two different forms of photon propagators. The constructed theory is used to find the thermal Coulomb potential and its asymptotic at large distances. Finally, the thermal effects of the lowest order in the fine structure constant and temperature are discussed in detail. Such effects are represented by the thermal one-photon exchange between a bound electron and the nucleus, thermal one-loop self-energy, thermal vacuum polarization, and recoil corrections and that of the finite size of the nucleus. Introduction of regularization allows one to avoid applying the renormalization procedure. To confirm this, the thermal vertex (with one, two, and three vertices) corrections are also described within the adiabatic S-matrix formalism. Finally, the paper discusses the influence of thermal effects on the finding of the proton radius and Rydberg constant.