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Teoreticheskaya i Matematicheskaya Fizika, 2004, Volume 141, Number 3, Pages 348–357
DOI: https://doi.org/10.4213/tmf134
(Mi tmf134)
 

This article is cited in 1 scientific paper (total in 1 paper)

The Newton–Wigner Problem in the Relativistic Quantum Mechanics of Free Particles

O. I. Zavialov

Steklov Mathematical Institute, Russian Academy of Sciences
Full-text PDF (210 kB) Citations (1)
References:
Abstract: 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.
Received: 02.12.2003
Revised: 17.06.2004
English version:
Theoretical and Mathematical Physics, 2004, Volume 141, Issue 3, Pages 1631–1639
DOI: https://doi.org/10.1023/B:TAMP.0000049758.00056.1b
Bibliographic databases:
Language: Russian
Citation: O. I. Zavialov, “The Newton–Wigner Problem in the Relativistic Quantum Mechanics of Free Particles”, TMF, 141:3 (2004), 348–357; Theoret. and Math. Phys., 141:3 (2004), 1631–1639
Citation in format AMSBIB
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\jour Theoret. and Math. Phys.
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\pages 1631--1639
\crossref{https://doi.org/10.1023/B:TAMP.0000049758.00056.1b}
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  • https://www.mathnet.ru/eng/tmf134
  • https://doi.org/10.4213/tmf134
  • https://www.mathnet.ru/eng/tmf/v141/i3/p348
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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