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arXiv · hep-th/0509199

Covariant canonical quantization

Georg M. von Hippel·Mattias N. R. Wohlfarth
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Abstract

We present a manifestly covariant quantization procedure based on the de Donder--Weyl Hamiltonian formulation of classical field theory. This procedure agrees with conventional canonical quantization only if the parameter space is $d=1$ dimensional time. In $d>1$ dimensions, covariant canonical quantization requires a fundamental length scale, and any bosonic field generates a spinorial wave function, leading to the emergence of spinors as a byproduct of quantization. We provide a probabilistic interpretation of the wave functions for the fields, and apply the formalism to a number of simple examples. These show that covariant canonical quantization produces both the Klein-Gordon and the Dirac equation, while also predicting the existence of discrete towers of identically charged fermions with different masses. Covariant canonical quantization can thus be understood as a `first' or pre-quantization within the framework of conventional QFT.

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Georg M. von Hippel, Mattias N. R. Wohlfarth. 2006-06-09. Covariant canonical quantization. https://doi.org/10.1140/epjc%2Fs2006-02595-5

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