Properties of three position operators constructed from free spin-½ fields

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Abstract
We consider three position operators constructed from free spin-½ fields. The first operator is the field-quantized form of the Dirac position operator. The momentum-space form of this operator has terms corresponding to single pair production and single pair destruction. The second and third operators are constructed to eliminate the pair terms. The second operator has no obvious nonfield analog, but the third is the field-quantized form of the Newton-Wigner position operator. We discuss several properties of these three operators, including the velocities, matrix elements, the algebra with respect to the Poincaré generators, covariance, and the self-commutativity of the operator densities at spacelike-separated points. Our conclusion is that the first, Dirac-type operator has the best combination of properties.