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arXiv:quant-ph/0208072 · Journal of Physics A Mathematical and General

Trajectories and particle creation and annihilation in quantum field theory

Detlef D uuml rr, Sheldon Goldstein, Roderich Tumulka, Nino Zangh�

Published Mar 27, 2003• 97 citations
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Abstract

We develop a theory based on Bohmian mechanics in which particle world lines can begin and end. Such a theory provides a realist description of creation and annihilation events and thus a further step towards a 'beable-based' formulation of quantum field theory, as opposed to the usual 'observable-based' formulation which is plagued by the conceptual difficulties—such as the measurement problem—of quantum mechanics.

DOI
10.1088/0305-4470/36/14/315

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We develop a theory based on Bohmian mechanics in which particle world lines can begin and end. Such a theory provides a realist description of creation and annihilation events and thus a further step towards a 'beable-based' formulation of quantum field theory, as opposed to the usual 'observable-based' formulation which is plagued by the conceptual difficulties—such as the measurement problem—of quantum mechanics.
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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.
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We show that the Bohmian approach in terms of persisting particles that move on continuous trajectories following a deterministic law can be literally applied to quantum field theory. By means of the Dirac sea model—exemplified in the electron sector of the standard model neglecting radiation—we explain how starting from persisting particles, one is led to standard QFT employing creation and annihilation operators when tracking the dynamics with respect to a reference state, the so-called vacuum. Since on the level of wave functions, both formalisms are mathematically equivalent, this proposal provides for an ontology of QFT that includes a dynamics of individual processes, solves the measurement problem, and explains the appearance of creation and annihilation events. 1. Bohmian Mechanics from Quantum Mechanics to Quantum Field Theory2. The Dirac Sea Model3. Equilibrium States and the Vacuum4. Excitations of the Vacuum and the Fock Space Formalism5. The Appearance of Particle Creations and Annihilations6. The Merits of the Bohmian Approach