Covariant canonical quantization

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.

27 pages, REVTeX4, revised version

References in corpus (12)

• Accelerating Cosmologies from Compactification
• Canonical Structure of Classical Field Theory in the Polymomentum Phase Space
• The Poisson Bracket for Poisson Forms in Multisymplectic Field Theory
• De Donder-Weyl Equations and Multisymplectic Geometry
• DeDonder-Weyl theory and a hypercomplex extension of quantum mechanics to field theory
• Precanonical Quantization and the Schroedinger Wave Functional
• Deformation Quantization: Twenty Years After
• Precanonical quantization of Yang-Mills fields and the functional Schroedinger representation
• Covariant canonical quantization of fields and Bohmian mechanics
• Comments on Good's Proposal for New Rules of Quantization
• Covariant Hamiltonian field theory. Path integral quantization
• BV quantization of covariant (polysymplectic) Hamiltonian field theory

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