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arXiv:0901.4106

A geometrical dual to relativistic Bohmian mechanics - the multi particle case

Benjamin Koch

Published Jan 27, 2009• 4 citations
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Abstract

In this article it is shown that the fundamental equations of relativistic Bohmian mechanics for multiple bosonic particles have a dual description in terms of a classical theory of curved space-time. We further generalize the results to interactions with an external electromagnetic field, which corresponds to the minimally coupled Klein-Gordon equation.

DOI
10.48550/arxiv.0901.4106

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In this article it is shown that the fundamental equations of relativistic Bohmian mechanics for multiple bosonic particles have a dual description in terms of a classical theory of curved space-time. We further generalize the results to interactions with an external electromagnetic field, which corresponds to the minimally coupled Klein-Gordon equation.
Positive-energy solutions of the Klein-Gordon equation form a Hilbert space of holomorphic functions on the future tube. This domain is interpreted as an extended phase space for the associated classical particle, the extra dimensions being the time and a new variable related to the inverse equilibrium temperature in an associated canonical ensemble. This gives a compelling formulation of relativistic Bohmian mechanics where the "hidden variables" are simply the classical trajectories of the particle in phase space. Interactions may be included through "holomorphic gauge theory."
Conventional relativistic quantum mechanics, based on the Klein-Gordon equation, does not possess a natural probabilistic interpretation in configuration space. The Bohmian interpretation, in which probabilities play a secondary role, provides a viable interpretation of relativistic quantum mechanics. We formulate the Bohmian interpretation of many-particle wave functions in a Lorentz-covariant way. In contrast with the nonrelativistic case, the relativistic Bohmian interpretation may lead to measurable predictions on particle positions even when the conventional interpretation does not lead to such predictions. Key words: relativistic quantum mechanics, Klein-Gordon equation, Bohmian interpretation. 1