Abstract
The structure of operators that transform covariantly in Poincaré invariant quantum mechanical models is analyzed. These operators are shown to have an interaction dependence that comes from the geometry of the Poincaré group. The operators can be expressed in terms of matrix elements in a complete set of eigenstates of the mass and spin operators associated with the dynamical representation of the Poincaré group. The matrix elements are factored into geometrical coefficients (Clebsch-Gordan coefficients for the Poincaré group) and invariant matrix elements. The geometrical coefficients are fixed by the transformation properties of the operator and the eigenvalue spectrum of the mass and spin. The invariant matrix elements, which distinguish between different operators with the same transformation properties, are given in terms of a set of invariant form factors.
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