Position Operators and Localizability of Quantum Systems Described by Finite- and Infinite-Dimensional Wave Equations

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Abstract
The principles of quantum mechanics impose certain restrictions on acceptable position operators. The probability density as derived from the position operator should agree with the fourth component of the current vector. The various relativistic wave equations are reexamined from the point of view of this consistency test. These and the group theoretical considerations lead to the conclusion that only a Dirac particle can be considered to be elementary. The position operator of the infinite-dimensional theories is investigated and the advantages of theories using the unitary representations of the Lorentz group are discussed.