  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.
