1999/03/28 by A. J. Bracken, A J Bracken, G. F. Melloy +1
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Electron #Observable #Operator (biology) #Point (geometry) #Position (finance) #Quantum Mechanics and Non-Hermitian Physics #Quantum and Classical Electrodynamics #Transformation (genetics) #quant-ph
paper · pdf · doi:10.1088/0305-4470/32/34/302
published as J.Phys.A32:6127-6139,1999 · 19 pages including 1 figure (1 LatTex2e file, 1 postscript file). Uses package amssymb. Typos corrected
arxiv created 1999/03/28 · openalex publication_date 1999/08/13 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 x . It is shown that, although x is not an observable in the usual sense, and has no positive-energy (generalized) eigenstates, the four-vector density ( ( x , t ), j ( x , t )/ c ) 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.