The dispersion relations are derived for the non-forward amplitudes for photon-proton scattering. By expanding these relations in momentum transfer and retaining first few terms, the dispersion relations for six independent combinations of the partial wave amplitudes are obtained. Contributions of the unphysical region are calculated to the first order in the fine structure constant, and are found to be consistent with the low energy theorem. Using these relations and photopion production data, the differential cross sections are calculated. In doing this, the amplitudes for the mixtures of dipole and quadrupole waves are taken into account in addition to electric dipole, electric quadrupole and magnetic dipole amplitudes. The results turn out to be fairly improved compared with the dipole model, and roughly explain experiments.