HIGH-ENERGY BEHAVIOR OF THE MEMBRANE SCATTERING-AMPLITUDES

High-energy behavior of the membrane scattering amplitudes is studied for two-body, fixed-angle, scattering processes. With the saddle point method, estimation of the amplitudes is performed under the assumptio n that the world volume appearing in the intermediate stage of the sca ttering is the simple S3 or T3. By taking the first case of sphere S3, analytical estimation of the amplitude is possible, whereas in the la tter case of torus T3, numerical analysis is necessary with the help o f the Ewald method developed in crystal physics and Monte Carlo simula ted annealing. The appearance of effects like structural phase transit ion is suggested for the membrane scattering amplitudes under the chan ge of the scattering angle.