The nucleon strange vector and isoscalar electromagnetic form factors are studied using a spectral decomposition. The Kbar{K} contribution to the electric and magnetic radii as well as the magnetic moment is evaluated to all orders in the strong interaction using an analytic continuation of experimental KN scattering amplitudes and bounds from unitarity. The relationship between non-resonant and resonant Kbar{K} contributions to the form factors is demonstrated, and values for the vector and tensor phi Nbar{N} couplings are derived. The Kbar{K} spectral functions are used to evaluate the credibility of model calculations for the strange quark vector current form factors.
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