Theory of the Electro- and Photoproduction ofπMesons

The scattering amplitude for the electroproduction of pions from nucleons is derived using the Mandelstam representation. It is shown that the amplitude consists mainly of two parts which in the framework of the Cini-Fubini approximation are simply additive. One part describes the effects of a $\pi -\pi$ resonance, while the other part describes the $\frac{3}{2}-\frac{3}{2}$ resonant nucleon term. The theory is fully relativistic in the sense that no expansion in inverse powers of the nucleon mass is made. This means that even though the theory is applicable only in the low-energy region where the $\frac{3}{2}-\frac{3}{2}$ resonance dominates, the momentum transfer variable upon which the various form factors depend, may be very large. The meson-current Born term contains explicitly the form factor of the pion and can be isolated at high momentum transfers to the electrons, where the resonant nucleon term becomes small.