Geodesic
The Newton--Wigner Problem in the Relativistic Quantum Mechanics of Free Particles
Teoretičeskaâ i matematičeskaâ fizika, Tome 141 (2004) no. 3, pp. 348-357

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We discuss the old Newton–Wigner problem, which is understood as the problem of a correct coordinate interpretation of the relativistic quantum mechanics of free particles. This problem is still relevant for quantum field theory because the $S$-matrix approach assumes that asymptotic fields describe relativistic free quantum-mechanical particles. From the modern standpoint, the original solution of this problem by Newton and Wigner already cannot be considered sufficient because it admits the smearing of wave packets with a superlight velocity. We discuss a possibility of overcoming this difficulty. This possibility is connected with relativistic deformations of the standard Heisenberg algebra. We describe situations in which a sort of desingularization of the effective free Hamiltonian occurs for some special deformations, which possibly allows preserving sublight velocity in the theory.
Keywords: Newton–Wigner operator, microscopic causality. 
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     author = {O. I. Zavialov},
     title = {The {Newton--Wigner} {Problem} in the {Relativistic} {Quantum} {Mechanics} of {Free} {Particles}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     number = {3},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2004_141_3_a1/}
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O. I. Zavialov. The Newton--Wigner Problem in the Relativistic Quantum Mechanics of Free Particles. Teoretičeskaâ i matematičeskaâ fizika, Tome 141 (2004) no. 3, pp. 348-357. http://geodesic.mathdoc.fr/item/TMF_2004_141_3_a1/