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

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.