Position and Intrinsic Spin Operators in Quantum Theory

Abstract

The problem of defining position and intrinsic spin operators in terms of the generators of the inhomogeneous Lorentz group is considered. These operators are taken to have the properties usually attributed to them in nonrelativistic quantum theory: their commutation relations must have the commonly accepted form. These commutation relations are then shown to define the intrinsic spin uniquely. The position operator is shown to be also essentially uniquely determined. Explicit forms of the spin and position operators for some special representations are exhibited. The relation of these operators to the spin and position operators of the spin-½ Dirac theory in the Foldy-Wouthuysen representation is considered. An Appendix gives a heuristic derivation of the spin operator.