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arXiv:hep-th/0610138 · Journal of Physics Conference Series

Bohmian mechanics in relativistic quantum mechanics, quantum field theory and string theory

Hrvoje Nikolić

Published May 1, 2007• 27 citations
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Abstract

I present a short overview of my recent achievements on the Bohmian interpretation of relativistic quantum mechanics, quantum field theory and string theory. This includes the relativistic-covariant Bohmian equations for particle trajectories, the problem of particle creation and destruction, the Bohmian interpretation of fermionic fields and the intrinsically Bohmian quantization of fields and strings based on the De Donder-Weyl covariant canonical formalism.

DOI
10.1088/1742-6596/67/1/012035

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I present a short overview of my recent achievements on the Bohmian interpretation of relativistic quantum mechanics, quantum field theory and string theory. This includes the relativistic-covariant Bohmian equations for particle trajectories, the problem of particle creation and destruction, the Bohmian interpretation of fermionic fields and the intrinsically Bohmian quantization of fields and strings based on the De Donder-Weyl covariant canonical formalism.
We formulate Bohmian mechanics (BM) such that the main objects of concern are macroscopic phenomena, while microscopic particle trajectories only play an auxiliary role. Such a formulation makes it easy to understand why BM always makes the same measurable predictions as standard quantum mechanics (QM), irrespective of the details of microscopic trajectories. Relativistic quantum field theory (QFT) is interpreted as an effective long-distance theory that at smaller distances must be replaced by some more fundamental theory. Analogy with condensed-matter physics suggests that this more fundamental theory could have a form of nonrelativistic QM, offering a simple generic resolution of an apparent conflict between BM and relativistic QFT.
We discuss a recently proposed extension of Bohmian mechanics to quantum field theory. For more or less any regularized quantum field theory there is a corresponding theory of particle motion, which, in particular, ascribes trajectories to the electrons or whatever sort of particles the quantum field theory is about. Corresponding to the nonconservation of the particle number operator in the quantum field theory, the theory describes explicit creation and annihilation events: the world lines for the particles can begin and end.
The biggest and most lasting among David Bohm's (1917-1992) many achievements is to have proposed a picture of reality that explains the empirical rules of quantum mechanics. This picture, known as pilot wave theory or Bohmian mechanics among other names, is still the simplest and most convincing explanation available. According to this theory, electrons are point particles in the literal sense and move along trajectories governed by Bohm's equation of motion. In this paper, I describe some more recent developments and extensions of Bohmian mechanics, concerning in particular relativistic space-time and particle creation and annihilation.
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
Abstract. I present a relativistic covariant version of the Bohmian interpretation of quantum mechanics and discuss the corresponding measurable predictions. The covariance is incoded in the fact that the nonlocal quantum potential transforms as a scalar, which is a consequence of the fact that the nonlocal wave function transforms as a scalar. The measurable predictions that can be obtained with the deterministic Bohmian interpretation cannot be obtained with the conventional interpretation simply because the conventional probabilistic interpretation does not work in the case of relativistic quantum mechanics.