## Double dispersion relation and unitarity as the basis for a dynamical theory of strong interactions |

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analytic function approximation arbitrary parameters asymptotic behavior attractive force barycentric system barycentric-system variables baryon bound calculate CDD pole complete complex plane configurations contribution corresponding coupling constant crossing symmetry delta function denominator function determined discontinuity double spectral functions dynamical elastic scattering electromagnetic structure energy equation exchange experimental Feynman diagrams Formula V.l Frazer and Fulco helicity amplitudes ill.l imaginary incomplete theory inelastic infinity integral intermediate invariant amplitude isotopic spin it-it it-N left-hand cut Lorentz invariance Mandelstam representation mass matrix element multiparticle n-p scattering nucleon nucleon-nucleon nucleon-photon vertex P-wave partial-wave amplitude phase shift photon physical region pion pairs pion-nucleon pion-pion polynomial expansion positive real axis possible potential problem quantum numbers reactions renormalizable repulsive residue resonance right-hand cut rt-rt S-matrix approach scalar scattering amplitude Sl sl strong interactions substitution law subtraction three channels three-pion threshold two-pion unitarity unitarity condition unphysical singularities vanish vector vertex function zero spin