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Localizing the Relativistic Electron

A. J. Bracken·G. F. Melloy
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Abstract

A causally well-behaved solution of the localization problem for the free electron is given, with natural space-time transformation properties, in terms of Dirac's position operator. It is shown that, although this operator does not represent an observable in the usual sense, and has no positive-energy (generalized) eigenstates, the associated 4-vector density is observable, and can be localized arbitrarily precisely about any point in space, at any instant of time, using only positive-energy states. A suitable spin operator can be diagonalized at the same time.

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A. J. Bracken, G. F. Melloy. 1999-03-28. Localizing the Relativistic Electron. https://doi.org/10.1088/0305-4470%2F32%2F34%2F302

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