The Mass Operator in the Light-Cone Representation

TL;DR

This paper identifies a previously omitted term in the matter density operator in light-cone representation for fermions with mass, reconciling results with equal-time calculations and discussing its effective operator form in DLCQ.

Contribution

It introduces a new term in the light-cone matter density operator for massive fermions, improving the consistency of theoretical predictions.

Findings

The new term aligns light-cone results with equal-time perturbation theory.

Effective operator representation in DLCQ captures the physics of the new term.

The form and coefficient of the term are challenging to determine from symmetry.

Abstract

I argue that for the case of fermions with nonzero bare mass there is a term in the matter density operator in the light-cone representation which has been omitted from previous calculations. The new term provides agreement with previous results in the equal-time representation for mass perturbation theory in the massive Schwinger model. For the DLCQ case the physics of the new term can be represented by an effective operator which acts in the DLCQ subspace, but the form of the term might be hard to guess and I do not know how to determine its coefficient from symmetry considerations.