FUNCTIONAL SCHRODINGER-EQUATION APPROACH TO HIGH-ENERGY MULTILEG AMPLITUDES

We use functional Schrodinger equation techniques, both for lambdaphi4 theory (no tunneling) and for B + L violation in SU(2) gauge theory, to estimate amplitudes for the decay of one off-shell particle into N on-shell particles, in the fixed-angle regime, when Nlambda greater-than-or-equal-to 1 (lambdaphi4) or at the sphaleron energy approximately M(W)/alpha(W) for gauge theory. The results, based for lambdaphi4 theory on a mean-gradient approach approximate for large N (small lambda) and for gauge theory on an accurate picture of the ground-state wave functional for large potentials, are that in lambdaphi4 theory the leading behavior of such an amplitude is e(-betaN), beta approximately 1, while in gauge, theory the (B + L)-violating cross section is suppressed by e(-2pi/alphaW), with an exponent 1/2 the 't Hooft exponent.