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We report on a spin-polarized inelastic neutron-scattering study of spin waves in the antiferromagnetically ordered state of BaFe_{2}As_{2}. Three distinct excitation components are identified, with spins fluctuating along the c axis, perpendicular to the ordering direction in the ab plane and parallel to the ordering direction. While the first two “transverse” components can be described by a linear spin-wave theory with magnetic anisotropy and interlayer coupling, the third “longitudinal” component is generically incompatible with the local-moment picture. It points toward a contribution of itinerant electrons to the magnetism that is already in the parent compound of this family of Fe-based superconductors.