Rigorous Lower Bound on the Kawarabayashi-Suzuki-Riazuddin-Fayyazuddin Relation from Field Theory: The Status of Field-Current Identity for Interacting Fields

Abstract

The possibility of retaining the axial-vector field-current identity for interacting $\ensuremath{\pi}$ and ${A}_{1}$ fields which are dynamically independent in the sense that $[{a}_{\ensuremath{\mu}}, \ensuremath{\pi}]=0$ and $[{a}_{\ensuremath{\mu}}, \stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\pi}}]=0$ at equal times is shown to lead to an inconsistency unless the mass of the pion is zero. A lower bound on the parameter $\frac{{G}_{\ensuremath{\rho}}}{(\sqrt{2}{m}_{\ensuremath{\rho}}{F}_{\ensuremath{\pi}})}$ is established for massless pions.