Abstract
The Bethe-Salpeter equation for the electrmagnetic bound state of two fermions is considered in a large class of covariant and axial gauges. To facilitate this study, we find it convenient to recast the B-S equation into a form such that the relative time coordinate has been eliminated. We thus obtain an exact single-time bound state equation, equal in content to the B-S equation, which can be treated by techniques familiar from Schrödinger theory. Using this equation, we find, in these nonradiation gauges, that there are an infinite number of B-S kernels contributing at O( m( Zα) 3ln( Zα) −1) or O( m( Zα) 3) to the bound state energy. We show that one can establish a pairwise cancellation of these contributions resulting in no net O( m( Zα) 3ln( Zα) −1) or O( m( Zα) 3) contributions to the energy. This is in agreement with results obtained in the radiation gauge and with results experimentally observed. The appearance of an infinite number of kernels contributing at this low order in Zα reflects the presence of noninstantaneous pieces in the photon propagator in these nonradiation gauges and exposes the difficulties encountered in attempting to do bound state calculations in such gauges.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
