The Wilson loop in light-front quantization

TL;DR

This paper explores the calculation of the Wilson loop in light-front quantization of QED, revealing an order-dependent ambiguity similar to that in the static photon propagator, and compares it with instant-form results.

Contribution

It applies Dirac's method to quantize QED in light-front gauge and analyzes the Wilson loop, highlighting an order-dependent ambiguity in the static limit.

Findings

Wilson loop matches known results only with specific order of limits

Ambiguity also appears in static photon propagator in coordinate space

Order of limits affects the equivalence between quantization schemes

Abstract

Using Dirac's method for the quantization of constrained systems QED is canonically quantized in the front-form in a gauge which is the light-front analog of the Weyl gauge. From the obtained vacuum wave functional the spatial Wilson loop is calculated. The result known from the canonical instant-form quantization or from the covariant path integral quantization is found only if the static limit $x^+ \to 0$ is taken in a specific order. The same ambiguity is also found in the static photon propagator in coordinate space.