(In-) consistencies in the Relativistic Description of Excited States in the Bethe–Salpeter Equation

✍ Scribed by Steven Ahlig; Reinhard Alkofer

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 400 KB
• Volume: 275
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1006/aphy.1999.5922

✦ Synopsis

The Bethe Salpeter equation provides the most widely used technique to extract bound states and resonances in a relativistic quantum field theory. Nevertheless a thorough discussion of how to identify its solutions with physical states is still missing. The occurrence of complex eigenvalues of the homogeneous Bethe Salpeter equation complicates this issue further. Using a perturbative expansion in the mass difference of the constituents we demonstrate for scalar fields bound by a scalar exchange that the underlying mechanism which results in complex eigenvalues is the crossing of a normal (or abnormal) with an abnormal state. Based on an investigation of the renormalization of one-particle properties we argue that these crossings happen beyond the applicability region of the ladder Bethe Salpeter equation. The implications for a fermion antifermion bound state in QED are discussed, and a consistent interpretation of the bound state spectrum of QED is proposed.