Ward-Takahashi identity in the light-front formalism for a bound state of fermions

TL;DR

This paper examines the Ward-Takahashi identity within the light-front formalism for a fermionic bound state, emphasizing the importance of zero modes and pair production diagrams for its validation.

Contribution

It demonstrates how to establish the Ward-Takahashi identity in the light-front formalism by analyzing zero modes and pair production diagrams for a fermionic bound state.

Findings

Zero modes are essential for the Ward-Takahashi identity in LF formalism.

Pair production diagrams play a crucial role in the identity's proof.

The identity holds when relevant LF momentum ranges are considered.

Abstract

We investigate the Ward-Takahashi identity at one-loop in the light-front (LF) formalism for a bound state of fermions. We consider a spinless bound state made up of two fermions in which the Ward-Takahashi identity is satisfied in the covariant formulation. Considering the same system in the light-front formalism, we investigate the proof of Ward-Takahashi identity by integrating the light-front energy component through the identification of the relevant ranges of the longitudinal LF momentum. We elucidate that the pair production diagram plays a crucial role in establishing the Ward-Takahashi identity. We also point out the necessity of taking into account the corresponding zero modes for truly establishing the Ward-Takahashi identity in the LF formalism.