Quantization of a New Canonical, Covariant, and Symplectic Hamiltonian Density
Abstract
We generalize Koopman-von Neumann classical mechanics to poly-symplectic fields and recover De Donder-Weyl theory. Comparing with Dirac's Hamiltonian density inspires a new Hamiltonian formulation with a canonical momentum field that is Lorentz covariant with symplectic geometry. We provide commutation relations for the classical and quantum fields that generalize the Koopman-von Neumann and Heisenberg algebras. The classical algebra requires four fields that generalize space-time, energy-momentum, frequency-wavenumber, and the Fourier conjugate of energy-momentum. We clarify how 1st and 2nd quantization can be found by simply mapping between operators in classical and quantum commutator algebras.
Keywords
Cite
@article{arxiv.2305.08864,
title = {Quantization of a New Canonical, Covariant, and Symplectic Hamiltonian Density},
author = {David Chester and Xerxes D. Arsiwalla and Louis Kauffman and Michel Planat and Klee Irwin},
journal= {arXiv preprint arXiv:2305.08864},
year = {2023}
}
Comments
27 pages including appendices and references