Covariant canonical quantization

TL;DR

This paper introduces a covariant quantization method based on the de Donder--Weyl Hamiltonian formulation, which naturally produces spinors, the Dirac equation, and predicts new fermionic states, extending quantum field theory.

Contribution

It develops a covariant canonical quantization framework that generalizes conventional methods to higher dimensions and reveals spinor emergence and new fermionic states.

Findings

Produces Klein-Gordon and Dirac equations from the formalism.

Requires a fundamental length scale in higher dimensions.

Predicts discrete towers of charged fermions with different masses.

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.