Return Path Propagation


		Garnet N. Ord *Department of Math, Physics and Computer Science*
Main Research Interests Overview Return Path Propagation Schroedinger's Equation The Dirac Equation Courses Calculus II (MTH240) Numerical Methods I (MTH510) Links Dr. L. Nottale (Fractal Space-time) Dr. S. Goldstein (Foundations, Bohm) Dr. D. Finklestein (Quantum Topology) Perimeter Institute Fields Institute Ryerson Home MPCS Home		Return Path Propagation This section contains abstracts of representative papers: Entwined Pairs and Schroedinger 's Equation Quantum Physics, abstract quant-ph/0206095 Authors: G.N. Ord, R.B. Mann Comments: 16 pg. 1 fig Journal-ref: Annals of Physics, (2004), to appear. We show that a point particle moving in space-time on entwined-pair paths generates Schroedinger's equation in a static potential in the appropriate continuum linit. This provides a new realist context for the Schroedinger equation within the domain of classical stochastic processes. It also suggests that self-quantizing systems may provide considerable insight into conventional quantum mechanics. Entwined Paths, Difference Equations and the Dirac Equation Quantum Physics, abstract quant-ph/0208004 Authors: G.N. Ord, R.B. Mann Comments: 15 pages, 5 figures Replacement 11/02 contains minor editorial changes Journal-ref: Phys.Rev.A. 67 (2003) Entwined space-time paths are bound pairs of trajectories which are traversed in opposite directions with respect to macroscopic time. In this paper we show that ensembles of entwined paths on a discrete space-time lattice are simply described by coupled difference equations which are discrete versions of the Dirac equation. There is no analytic continuation, explicit or forced, involved in this description. The entwined paths are `self-quantizing'. We also show that simple classical stochastic processes that generate the difference equations as ensemble averages are stable numerically and converge at a rate governed by the details of the stochastic process. This result establishes the Dirac equation in one dimension as a phenomenological equation describing an underlying classical stochastic process in the same sense that the Diffusion and Telegraph equations are phenomenological descriptions of stochastic processes. The Feynman Propagator from a Single Path Quantum Physics, abstract quant-ph/0109092 Authors: G. N. Ord, J. A. Gualtieri Comments: 4 pages, 3 figures Journal-ref: Phys.Rev.Lett. 89 (2002) 250403 We show that is possible to construct the Feynman Propagator for a free particle in one dimension, without quantization, from a single continuous space-time path. The animation shows the time evolution of the Feynman Chessboard propagator from the Feynman ensemble of paths (red) with the same calculation from a single space-time path (black dots).