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arXiv · 2305.08864

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

David Chester·Xerxes D. Arsiwalla·Louis Kauffman·Michel Planat·Klee Irwin
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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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David Chester, Xerxes D. Arsiwalla, Louis Kauffman, Michel Planat, Klee Irwin. 2023-05-05. Quantization of a New Canonical, Covariant, and Symplectic Hamiltonian Density. https://arxiv.org/abs/2305.08864

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