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Quantization via hopping amplitudes: Schroedinger equation and free QED

L. Polley
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Abstract

Schroedinger's equation with scalar and vector potentials is shown to describe "nothing but" hopping of a quantum particle on a lattice; any spatial variation of the hopping amplitudes acts like an external electric and/or magnetic field. The main point of the argument is the superposition principle for state vectors; Lagrangians, path integrals, or classical Hamiltonians are not (!) required. Analogously, the Hamiltonian of the free electromagnetic field is obtained as a twofold continuum limit of unitary hopping in Z(N) link configuration space, if gauge invariance and C and P symmetries are imposed.

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L. Polley. 2000-03-03. Quantization via hopping amplitudes: Schroedinger equation and free QED. https://arxiv.org/abs/quant-ph/9907102

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