dorsal/arxiv
View SchemaEntwined Paths, Difference Equations and the Dirac Equation
| Authors | G. N. Ord, R. B. Mann |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0208004 |
| URL | https://arxiv.org/abs/quant-ph/0208004 |
| DOI | 10.1103/PhysRevA.67.022105 |
Abstract
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.
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"abstract": "Entwined space-time paths are bound pairs of trajectories which are traversed\nin opposite directions with respect to macroscopic time. In this paper we show\nthat ensembles of entwined paths on a discrete space-time lattice are simply\ndescribed by coupled difference equations which are discrete versions of the\nDirac equation. There is no analytic continuation, explicit or forced, involved\nin this description. The entwined paths are `self-quantizing\u0027. We also show\nthat simple classical stochastic processes that generate the difference\nequations as ensemble averages are stable numerically and converge at a rate\ngoverned by the details of the stochastic process. This result establishes the\nDirac equation in one dimension as a phenomenological equation describing an\nunderlying classical stochastic process in the same sense that the Diffusion\nand Telegraph equations are phenomenological descriptions of stochastic\nprocesses.",
"arxiv_id": "quant-ph/0208004",
"authors": [
"G. N. Ord",
"R. B. Mann"
],
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"quant-ph"
],
"doi": "10.1103/PhysRevA.67.022105",
"title": "Entwined Paths, Difference Equations and the Dirac Equation",
"url": "https://arxiv.org/abs/quant-ph/0208004"
},
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