Causality in the relativistic bound-state problem

TL;DR

This paper discusses how preserving field-redefinition invariance in truncated Bethe-Salpeter equations may resolve inconsistencies in relativistic bound-state problems, with a focus on a light-by-light scattering sum rule as a test.

Contribution

It proposes that maintaining field-redefinition invariance in truncations of the Bethe-Salpeter equation can address common issues in relativistic bound-state calculations.

Findings

Sum rule for light-by-light scattering as a testing tool

Field-redefinition invariance preserves symmetries in truncations

Potential resolution of one-body limit issues

Abstract

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.