GAUGE-INVARIANCE AND BINDING-ENERGY REGULARIZATION OF BOUND-STATE INFRARED DIVERGENCES

We discuss the discrepancy between the Cung et al. [Phys. Lett. B 68, 474 (1977)] calculation of the three-photon-annihilation contribution to the positronium ground-state energy, performed using the binding energy to regulate the infrared divergences, and the recent calculation of Adkins, Bui, and Zhu [Phys. Rev. A 37, 4071 (1988)], which used a photon mass to regulate these divergences. By using a simpler version of the binding-energy approach advocated by these authors, we confirm the value of the discrepancy they obtained. Furthermore, it is shown that the additional term needed in the binding-energy approach to produce agreement between the two methods is precisely the one required to make the binding-energy regularized amplitudes gauge invariant to all orders in the binding. © 1990 The American Physical Society.