QED$_{4}$ Ward Identity for fermionic field in the light-front

TL;DR

This paper investigates the role of contact terms in the fermionic propagator within light-front quantum field theory and their impact on the Ward identity, crucial for gauge invariance.

Contribution

It analyzes the effect of removing contact terms from the fermion propagator on the Ward identity in light-front QED, highlighting their significance.

Findings

Contact terms are essential for maintaining the Ward identity in light-front formulations.

Dropping contact terms affects the gauge invariance properties of the fermionic propagator.

The study clarifies the role of non-propagating components in relativistic quantum field theories.

Abstract

In a covariant gauge we implicitly assume that the Green's function propagates information from one point of the space-time to another, so that the Green's function is responsible for the dynamics of the relativistic particle. In the light front form, which in principle is a change of coordinates, one would expect that this feature would be preserved. In this manner, the fermion's field propagator can be split into a propagating piece and a non-propagating (``contact'') term. Since the latter (``contact'') one does not propagate information, and therefore, assumedly with no harm to the field dynamics we wanted to know what would be the impact of dropping it off. To do that, we investigated its role in the Ward identity in the light front.