(In-)Consistencies in the relativistic description of excited states in the Bethe-Salpeter equation

Abstract

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 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.

39 pages, 14 figures, LaTeX2e, uses amssymb, minor changes, references added, to appear in Annals Phys

References in corpus (2)

• Is there a Landau Pole Problem in QED?
• Bethe-Salpeter equation: 3D reductions, heavy mass limits and abnormal solutions

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