Abstract
The localization problem in relativistic quantum mechanics consists in finding (i) the operator representative X k of position and/or its eigenstates (called localized states), (ii) their properties and (iii) the representatives and properties of variables related to position such, as time, proper time and velocity. We devote this review mainly to position and briefly to variables like velocity. Time and proper time will be discussed only when relevant to position.
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If an author chose (i) as his approach and confirms his results through (ii), he will be only quoted when writing the properties he used as axioms.
The set is not exhaustive. Some properties were not listed because of difficulties of systematization.
This requirement has different forms: If X is an operator, it means that X be a 4-vector operator; if X is a c-number, it only means the appropriate transformation properties of mean values.
However it should not be imposed on the neutrino. See Ref. [13].
However if (b 1) is rejected the behaviour of position under translations is not clear.
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The physical reason is that the time in which a quantum experiment is done is measured as the classical time of the (macroscopic) frame of reference.
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See Section 3 of Ref. [60].
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FLEMING, G. N.: Phys. Rev. ID, 542 (1970).
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Kálnay, A.J. (1971). The Localization Problem. In: Bunge, M. (eds) Problems in the Foundations of Physics. Studies in the Foundations, Methodology and Philosophy of Science, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80624-7_7
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