Relation between the Vertex Function and the Propagators in the Pseudovector Coupling Pion-Nucleon System

TL;DR

This paper derives a complex Ward-Takahashi identity for the pseudovector pion-nucleon system, revealing intricate relations between the vertex function and propagators, with implications for understanding non-conserved currents.

Contribution

It provides a closed-form relation between the vertex function and propagators in a non-conserved current system, extending the Ward-Takahashi identity beyond QED.

Findings

Derived the Ward-Takahashi identity for the pseudovector pion-nucleon system.

Revealed complex relations between vertex functions and propagators.

Identified interesting results in propagator behavior within the system.

Abstract

The procedure for deriving the Ward-Takahashi identity is applied to the pseudovector coupling pion-nucleon system in which the isovector and axial-vector current does not conserved. The relation is given in closed form although it is more complicated than that of the quantum electrodynamics. The application to the propagator has revealed the interesting results.