Physics – Quantum Physics
Scientific paper
1999-03-28
J.Phys.A32:6127-6139,1999
Physics
Quantum Physics
19 pages including 1 figure (1 LatTex2e file, 1 postscript file). Uses package amssymb. Typos corrected
Scientific paper
10.1088/0305-4470/32/34/302
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.
Bracken Anthony J.
Melloy G. F.
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