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

2023/05/05 by Chester, David, Arsiwalla, Xerxes D., Kauffman, Louis +2 · 1 citation
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2305.08864

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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