Eur. Phys. J. C (2006) 47: 861-872
https://doi.org/10.1140/epjc/s2006-02595-5

Theoretical Physics

Covariant canonical quantization

¹ Department of Physics, University of Regina, 3737 Wascana Parkway, Regina, Saskatchewan, S4S 0A2, Canada
² Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, 22761, Hamburg, Germany

Received: 7 April 2006
Published online: 27 June 2006

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 quantization requires a fundamental length scale, and any bosonic field generates a spinorial wave function, leading to the purely quantum-theoretical emergence of spinors as a byproduct. We provide a probabilistic interpretation of the wave functions for the fields, and we 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.