Covariant canonical quantization

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. PACS 04.62.+v; 11.10.Ef; 12.10.Kt