1998/04/25 by George Jaroszkiewicz, Keith Norton, Jaroszkiewicz, George +1
Engineering · Physics and Astronomy · #Control and Stability of Dynamical Systems #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #gr-qc #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9804165
31 pages TCILateX
arxiv created 1998/04/25 · openalex publication_date 1998/04/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Principles of discrete time mechanics are applied to the quantisation of Maxwell's equations. Following an analysis of temporal node and link variables, we review the classical discrete time equations in the Coulomb and Lorentz gauges and conclude that electro-magneto duality does not occur in pure discrete time electromagnetism. We discuss the role of boundary conditions in our mechanics and how temporal discretisation should influence very early universe dynamics. Quantisation of the Maxwell potentials is approached via the discrete time Schwinger action principle and the Faddeev-Popov path integral. We demonstrate complete agreement in the case of the Coulomb gauge, obtaining the vacuum functional and the discrete time field commutators in that gauge. Finally, we use the Faddeev-Popov method to construct the discrete time analogues of the photon propagator in the Landau and Feynman gauges, which casts light on the break with relativity and possible discrete time analogues of the metric tensor.