Principles of Discrete Time Mechanics: I. Particle Systems

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dc.creatorJaroszkiewicz, George
dc.creatorNorton, Keith
dc.date1997-03-11
dc.date.accessioned2026-07-07T10:58:50Z
dc.date.available2026-07-07T10:58:50Z
dc.descriptionWe discuss the principles to be used in the construction of discrete time classical and quantum mechanics as applied to point particle systems. In the classical theory this includes the concept of virtual path and the construction of system functions from classical Lagrangians, Cadzow's variational principle applied to the action sum, Maeda-Noether and Logan invariants of the motion, elliptic and hyperbolic harmonic oscillator behaviour, gauge invariant electrodynamics and charge conservation, and the Grassmannian oscillator. First quantised discrete time mechanics is discussed via the concept of system amplitude, which permits the construction of all quantities of interest such as commutators and scattering amplitudes. We discuss stroboscopic quantum mechanics, or the construction of discrete time quantum theory from continuous time quantum theory and show how this works in detail for the free Newtonian particle. We conclude with an application of the Schwinger action principle to the important case of the quantised discrete time inhomogeneous oscillator.
dc.description35 pages, LateX, To be published in J.Phys.A: Math.Gen. Basic principles stated: applications to field theory in subsequent papers of series contact email address: jag@maths.nott.ac.uk
dc.identifierhttps://arxiv.org/abs/hep-th/9703079
dc.identifierhttp://arxiv.org/abs/hep-th/9703079
dc.identifierJ.Phys.A30:3115-3144,1997
dc.identifierdoi:10.1088/0305-4470/30/9/022
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/187244
dc.subjectHigh Energy Physics - Theory
dc.subjectQuantum Physics
dc.titlePrinciples of Discrete Time Mechanics: I. Particle Systems
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