Why pair production cures covariance in the light-front?

TL;DR

This paper demonstrates that considering the complete Fock space in light-front quantum field theory restores covariance and resolves issues with the vacuum structure, using electromagnetic current calculations for scalar bosons as an example.

Contribution

It introduces a method to restore covariance in light-front theories by including the full Fock space, eliminating the need for ad hoc pole dislocation prescriptions.

Findings

Covariance is restored when the complete Fock space is considered.

The electromagnetic current for scalar bosons is constructed in the light-front framework.

Dislocating the integration pole is a special case of the complete Fock space approach.

Abstract

We show that the light-front vaccum is not trivial, and the Fock space for positive energy quanta solutions is not complete. As an example of this non triviality we have calculated the electromagnetic current for scalar bosons in the background field method were the covariance is restored through considering the complete Fock space of solutions. We also show thus that the method of "dislocating the integration pole" is nothing more than a particular case of this, so that such an "ad hoc" prescription can be dispensed altogether if we deal with the whole Fock space. In this work we construct the electromagnetic current operator for a system composed of two free bosons. The technique employed to deduce these operators is through the definition of global propagators in the light front when a background electromagnetic field acts on one of the particles.