Causality in the Relativistic Bound-State Problem

Although the exact Bethe–Salpeter equation is certainly the appropriate field-theoretic framework to describe the non-perturbative problem of scattering and bound states, the inevitable truncations introduce inconsistencies such as loss of symmetries or incorrect one-body limit. I conjecture that these problem can be overcome if the truncation preserves the field-redefinition invariance of the exact equation. A sum rule for light-by-light scattering can provide a testing ground of this conjecture.