Analytic solution of the microcausality problem in Discretized Light Cone Quantization

TL;DR

This paper demonstrates that causality violations in discretized light-cone quantization are negligible and disappear as the volume approaches infinity, providing an exact integral representation for two-point functions.

Contribution

It introduces an exact integral representation for two-point functions in finite volume light-front theories, showing causality violations vanish in the continuum limit.

Findings

Causality violation is marginal at finite volume.

Two-point functions recover continuum results as volume increases.

Violations smoothly vanish in the infinite volume limit.

Abstract

It is shown that that violation of causality in two-dimensional light-front field theories quantized in a finite ``volume'' $L$ with periodic or antiperiodic boundary conditions is marginal and vanishes smoothly in the continuum limit. For this purpose, we derive an exact integral representation for the complete infinite series expansion of the two-point functions of a free massive scalar and fermi field for an arbitrary finite value of $L$ and show that in the $L \to \infty$ limit we retrieve the correct continuum results.