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Physics Reports

The de Broglie-Bohm theory of motion and quantum field theory

Peter Holland

Published Mar 1, 1993• 109 citations
Publisher
DOI
10.1016/0370-1573(93)90095-u

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Abstract We generalize the de Broglie-Bohm (dBB) formulation of quantum mechanics to the case of quantum gravity (QG) by using the effective action for a QG theory. This is done by replacing the dBB equations of motion with the effective action equations of motion, which is beneficial even in the non-gravitational case, since in this way one avoids the violations of the Heisenberg uncertainity relations and the absence of the classical trajectories for stationary bound states. Another advantage of the effective action formalism is that one can obtain the field configurations in the case of a quantum field theory (QFT). The proposed QG generalization is natural for Bohmiam mechanics because a dBB wavefunction is really a wavefunction of the Universe and in order to define the effective action for an arbitrary initial state one needs a QG path integral. The QG effective action can be constructed by using the piecewise flat quantum gravity (PFQG) theory and the PFQG effective action can be approximated by the QFT effective action for General Relativity coupled to matter, with a cutoff determined by the average edge length of the spacetime triangulation. One can then calculate the corresponding field configurations and from these field configurations one can obtain the trajectories for the corresponding elementary particles.

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Supporters of the de Broglie-Bohm (dBB) interpretation of quantum theory argue that because the theory, like classical mechanics, concerns the motions of point particles in 3D space, it is specially suited to recover classical behavior. I offer a novel account of classicality in dBB theory, if only to show that such an account falls out almost trivially from results developed in the largely interpretation-neutral context of decoherence theory. I then argue that this undermines any special claim that dBB theory is purported to have on the unification of the quantum and classical realms.

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Modified de Broglie-Bohm approach to quantum mechanics

Moncy V. John

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Abstract We generalize the de Broglie-Bohm (dBB) formulation of quantum mechanics to the case of quantum gravity (QG) by using the effective action for a QG theory. This is done by replacing the dBB equations of motion with the effective action equations of motion, which is beneficial even in the non-gravitational case, since in this way one avoids the violations of the Heisenberg uncertainity relations and the absence of the classical trajectories for stationary bound states. Another advantage of the effective action formalism is that one can obtain the field configurations in the case of a quantum field theory (QFT). The proposed QG generalization is natural for Bohmiam mechanics because a dBB wavefunction is really a wavefunction of the Universe and in order to define the effective action for an arbitrary initial state one needs a QG path integral. The QG effective action can be constructed by using the piecewise flat quantum gravity (PFQG) theory and the PFQG effective action can be approximated by the QFT effective action for General Relativity coupled to matter, with a cutoff determined by the average edge length of the spacetime triangulation. One can then calculate the corresponding field configurations and from these field configurations one can obtain the trajectories for the corresponding elementary particles.
Supporters of the de Broglie-Bohm (dBB) interpretation of quantum theory argue that because the theory, like classical mechanics, concerns the motions of point particles in 3D space, it is specially suited to recover classical behavior. I offer a novel account of classicality in dBB theory, if only to show that such an account falls out almost trivially from results developed in the largely interpretation-neutral context of decoherence theory. I then argue that this undermines any special claim that dBB theory is purported to have on the unification of the quantum and classical realms.