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

A. T. Suzuki·J. H. O. Sales·G. E. R. Zambrano
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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.

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A. T. Suzuki, J. H. O. Sales, G. E. R. Zambrano. 2004-06-02. Surprises in the relativistic free-particle quantization on the light-front. https://arxiv.org/abs/hep-th/0405095

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