Principles of Discrete Time Mechanics: V. The Quantisation of Maxwell's Equations
Abstract
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 electromagneto 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 FaddeevPopov 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 FaddeevPopov 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.
 Publication:

arXiv eprints
 Pub Date:
 April 1998
 DOI:
 10.48550/arXiv.hepth/9804165
 arXiv:
 arXiv:hepth/9804165
 Bibcode:
 1998hep.th....4165J
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 31 pages TCILateX