Localizing the Relativistic Electron
Quantum Physics
2008-11-26 v1
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.
Cite
@article{arxiv.quant-ph/9903087,
title = {Localizing the Relativistic Electron},
author = {A. J. Bracken and G. F. Melloy},
journal= {arXiv preprint arXiv:quant-ph/9903087},
year = {2008}
}
Comments
19 pages including 1 figure (1 LatTex2e file, 1 postscript file). Uses package amssymb. Typos corrected