Disentangling Intertwined Embedded States and Spin Effects in Light-Front Quantization

TL;DR

This paper investigates the discrepancies in light-front quantization, revealing the necessity of subtracting nonvalence contributions to maintain covariance and current conservation, with numerical analysis for fermion and boson cases.

Contribution

It demonstrates the importance of subtracting nonvalence contributions in light-front quantization to recover covariant Feynman amplitudes, especially for fermion constituents.

Findings

Nonvalence contributions cause end-point singularities in fermion cases.

Subtracting nonvalence terms restores covariance and current conservation.

Boson constituents do not exhibit the singularity, matching Feynman amplitudes without adjustments.

Abstract

Naive light-front quantization, carried out by a light-front energy integration of covariant amplitudes, is not guaranteed to generate the corresponding Feynman amplitudes. In an explicit example we show that the nonvalence contribution to the minus-component of the EM current of a meson with fermion constituents has a persistent end-point singularity. Only after this term is subtracted, the result is covariant and satisfies current conservation. If the spin-1/2 constituents are replaced by spin zero ones, the singularity does not occur and the result is, without any adjustment, identical to the Feynman amplitude. Numerical estimates of valence and nonvalence contributions are presented for the cases of fermion and boson constituents.