Surprises in the relativistic free-particle quantization on the light-front

TL;DR

This paper investigates the quantization of a relativistic free particle on the light-front, revealing inconsistencies in the canonical commutation relations and proposing a remedy with significant implications for the quantization process.

Contribution

It identifies a fundamental inconsistency in light-front quantization and offers a simple solution, impacting the understanding of relativistic quantum systems.

Findings

Inconsistency found in light-front commutation relations

Proposed a remedy to the Poisson bracket definition

Implications for the physical interpretation of quantization

Abstract

We use the light front ``machinery'' to study the behavior of a relativistic free particle and obtain the quantum commutation relations from the classical Poisson brackets. We argue that their usual projection onto the light-front coordinates from the covariant commutation relations show that there is an inconsistency in the expected correlation between canonically conjugate variables ``time'' and ``energy''. Moreover we show that this incompatibility originates from the very definition of the Poisson brackets that is employed and present a simple remedy to this problem and envisages a profound physical implication on the whole process of quantization.