Quantization of a New Canonical, Covariant, and Symplectic Hamiltonian Density

• URL: http://arxiv.org/abs/2305.08864v2
• Date: Thu, 7 Sep 2023 21:48:27 GMT
• Title: Quantization of a New Canonical, Covariant, and Symplectic Hamiltonian Density
• Authors: David Chester, Xerxes D. Arsiwalla, Louis Kauffman, Michel Planat, and Klee Irwin
• Abstract summary: We generalize classical mechanics to poly-symplectic fields and recover De Donder-Weyl theory. We provide commutation relations for the classical and quantum fields that generalize the Koopman-von Neumann and Heisenberg algebras.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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