dorsal/arxiv
View Schemade Broglie's pilot wave theory for the Klein-Gordon equation
| Authors | G Horton, C Dewdney |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0109059 |
| URL | https://arxiv.org/abs/quant-ph/0109059 |
Abstract
We illustrate, using a simple model, that in the usual formulation the time-component of the Klein-Gordon current is not generally positive definite even if one restricts allowed solutions to those with positive frequencies. Since in de Broglie's theory of particle trajectories the particle follows the current this leads to difficulties of interpretation, with the appearance of trajectories which are closed loops in space-time and velocities not limited from above. We show that at least this pathology can be avoided if one uses a covariant extension of the canonical formulation of relativistic point particle dynamics proposed by Gitman and Tyutin.
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"abstract": "We illustrate, using a simple model, that in the usual formulation the\ntime-component of the Klein-Gordon current is not generally positive definite\neven if one restricts allowed solutions to those with positive frequencies.\nSince in de Broglie\u0027s theory of particle trajectories the particle follows the\ncurrent this leads to difficulties of interpretation, with the appearance of\ntrajectories which are closed loops in space-time and velocities not limited\nfrom above. We show that at least this pathology can be avoided if one uses a\ncovariant extension of the canonical formulation of relativistic point particle\ndynamics proposed by Gitman and Tyutin.",
"arxiv_id": "quant-ph/0109059",
"authors": [
"G Horton",
"C Dewdney"
],
"categories": [
"quant-ph"
],
"title": "de Broglie\u0027s pilot wave theory for the Klein-Gordon equation",
"url": "https://arxiv.org/abs/quant-ph/0109059"
},
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