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.
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REFERENCES
T. Newton and E. Wigner, Rev.Modern Phys., 21, 400 (1949).
J. von Neumann, Ann.Math., 50, 401 (1949).
M. H. L. Pryce, Proc.Roy.Soc.London,Ser.A, 195, 62 (1948); C. Moller, Ann.Inst.H.Poincar ´e, 11, 251 (1949); Commun.Dublin Inst.Adv.Studies,Ser.A, No. 5, 1 (1949); A. Papapetrou, Acad.Athens, 14, 540 (1939).
S. S. Schweber, An Introduction to Relativistic Quantum Field Theory, Row, Peterson and Co., Evanston, Ill. (1961).
A. A. Sokolov and I. M. Ternov, Relativistic Electron [in Russian], Nauka, Moscow (1974); English transl.: Radiation from Relativistic Electron, AIP, New York (1986).
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Zavialov, O.I. The Newton–Wigner Problem in the Relativistic Quantum Mechanics of Free Particles. Theoretical and Mathematical Physics 141, 1631–1639 (2004). https://doi.org/10.1023/B:TAMP.0000049758.00056.1b
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DOI: https://doi.org/10.1023/B:TAMP.0000049758.00056.1b