Putting positrons into classical Dirac field theory

2020

Phys. Rev. A

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Some authors have claimed that there exists a minimum size (on the order of the Compton radius) for electron states composed entirely of positive-frequency solutions to the free Dirac equation. Other authors have put forward counterexamples to such claims. This article asks how the counterexamples of A. J. Bracken and G. F. Melloy [J. Phys. A. 32, 6127 (1999)] bypass two arguments against their possibility. The first is an old argument that, because of the prohibition on faster-than-light motion, the electron must be larger than a certain minimum size if it is to have the correct angular momentum and magnetic moment. This challenge can be addressed by analyzing the flow of energy and charge for the counterexample states. The second argument is an explicit proof (presented in C.-P. Chuu et al. [Solid State Commun. 150, 533 (2010)]) that there is a minimum size for purely positive-frequency electron states. This proof hinges on the assumption of a small spread in momentum space, which is violated by the counterexamples that have been put forward.

Section: Discussionmentioning

confidence: 99%

Section: Small Electron Statesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…In Ref [1]. I argued that we should actually flip the sign of the charge density and charge current density for negative-frequency modes.…”

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confidence: 99%

See 3 more Smart Citations

Possibility of small electron states

2020

Phys. Rev. A

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Electron Charge Density: A Clue from Quantum Chemistry for Quantum Foundations

2021

Found Phys

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Within quantum chemistry, the electron clouds that surround nuclei in atoms and molecules are sometimes treated as clouds of probability and sometimes as clouds of charge. These two roles, tracing back to Schrödinger and Born, are in tension with one another but are not incompatible. Schrödinger's idea that the nucleus of an atom is surrounded by a spread-out electron charge density is supported by a variety of evidence from quantum chemistry, including two methods that are used to determine atomic and molecular structure: the Hartree-Fock method and density functional theory. Taking this evidence as a clue to the foundations of quantum physics, Schrödinger's electron charge density can be incorporated into many different interpretations of quantum mechanics (and extensions of such interpretations to quantum field theory).

The Disappearance and Reappearance of Potential Energy in Classical and Quantum Electrodynamics

2022

Found Phys

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In electrostatics, we can use either potential energy or field energy to ensure conservation of energy. In electrodynamics, the former option is unavailable. To ensure conservation of energy, we must attribute energy to the electromagnetic field and, in particular, to electromagnetic radiation. If we adopt the standard energy density for the electromagnetic field, then potential energy seems to disappear. However, a closer look at electrodynamics shows that this conclusion actually depends on the kind of matter being considered. Although we cannot get by without attributing energy to the electromagnetic field, matter may still have electromagnetic potential energy. Indeed, if we take the matter to be represented by the Dirac field (in a classical precursor to quantum electrodynamics), then it will possess potential energy (as can be seen by examining the symmetric energy-momentum tensor of the Dirac field). Thus, potential energy reappears. Upon field quantization, the potential energy of the Dirac field becomes an interaction term in the Hamiltonian operator of quantum electrodynamics.