FUNCTIONAL SCHRODINGER-EQUATION APPROACH TO HIGH-ENERGY MULTIPARTICLE SCATTERING

We summarize a series of arguments, based on semi-classical techniques, for calculating fixed-angle scattering amplitudes such as T2-->N in a weakly-coupled theory with coupling g2 much less than 1, and Ng2 greater-than-or-equal-to 1. These techniques are applied to the (functional) Schrodinger equation for the quartic oscillator, including the double well, and for d=4 field theories. The result is that for processes with no tunneling, T2-->N has the leading behavior exp(-alpha-N), alpha = O(1). (For the quartic oscillator, alpha=1/2pi.) For theories with tunneling, when the energy is at the top of the barrier, we make it plausible that T2-->N approximately exp(-1/2I), where I is the zero-energy (instanton) tunneling exponent.