Quantization via hopping amplitudes: Schroedinger equation and free QED

1999/07/30 by L. Polley, Polley, L.
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Quantum optics and atomic interactions #quant-ph

paper · pdf · doi:10.48550/arxiv.quant-ph/9907102

LaTeX2e, 12 pages, no figures

openalex publication_date 1999/07/30 · arxiv created 2000/03/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Quarks, Gluons and Lattices

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