Noncommuting spinor rotation due to balanced geometrical and dynamical phases

A neutron polarimetric textbook experiment is performed to demonstrate the noncommutation properties of the Pauli spin operator. The polarization of t he transmitted neutron beam depends upon the sequential order of two succes sive spin-flip devices with mutually inclined precession axes. Furthermore, an interpretation of the observed results is presented in terms of an intr insic phase shift between two interfering mutually orthogonal spin states, which in a sequence of two successive spinor transformations stores particu lar information about the intermediate state. This phase shift is discussed with respect to its geometrical and dynamical components, and its formal c onnection with the noncommuting properties of Pauli spin operators is expli citly shown. [S1050-2947(99)01806-5].