Relativistic free-particle quantization on the light-front: New aspects

TL;DR

This paper investigates the quantization of a relativistic free particle on the light-front, revealing that standard projection methods do not yield expected quantum commutation relations, thus highlighting new aspects of light-front quantization.

Contribution

It demonstrates that conventional projection onto light-front coordinates from covariant relations is insufficient, offering new insights into light-front quantization of relativistic particles.

Findings

Standard projection methods fail to reproduce expected commutation relations.

New aspects of light-front quantization are identified.

Classical Poisson brackets lead to specific quantum commutation relations.

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 the usual projection onto the light-front coordinates for these from the covariant commutation ralations does not reproduce the expected results.