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69:, are the premier notion of position in relativistic quantum mechanics of a single particle. They enjoy the same commutation relations with the 3 space momentum operators and transform under rotations in the same way as the
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in the relativistic setting that resembled the position operator in basic quantum mechanics in the sense that at low momenta it approximately agreed with that operator. It also has several famous strange behaviors (see the
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in particular), one of which is seen as the motivation for having to introduce quantum field theory.
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This ensures that the free particle moves at the expected velocity with the given momentum/energy.
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On the relativistic spatial localization for massive real scalar Klein–Gordon quantum particles
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106:, as the position in ordinary QM, they have additional properties: One of these is that
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Apparently these notions were discovered when attempting to define a
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41:. It is known to largely conflict with the
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16:Scheme for obtaining the position operator
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217:"Localized States for Elementary Systems"
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48:The Newton–Wigner position operators
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215:Newton, T.D.; Wigner, E.P. (1949).
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45:outside of a very limited scope.
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276:Lett Math Phys 113, 66 (2023).
357:Axiomatic quantum field theory
259:V. Bargmann and E. P. Wigner,
183:{\displaystyle =p_{i}/p_{0}~.}
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30:) is a scheme for obtaining a
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305:. You can help Knowledge by
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20:Newton–Wigner localization
242:10.1103/RevModPhys.21.400
221:Reviews of Modern Physics
24:Theodore Duddell Newton
301:-related article is a
261:Proc Natl Acad Sci USA
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43:Reeh–Schlieder theorem
362:Quantum physics stubs
198:self adjoint operator
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352:Quantum field theory
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266:, 211-223 (1948).
233:1949RvMP...21..400N
203:Hegerfeldt theorem
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