Quantum Scattering and Classical Solutions

I discuss a formalism for computing quantum scattering amplitudes using a semiclassical expansion of a functional integral representation for the S-matrix. The classical background for the expansion is determined by solving the equations of motion subject to nontrivial boundary conditions determined by the initial and final quantum states. The formalism is designed to accommodate intrinsically nonperturbative processes such as baryon number violation, quantum tunneling and multiparticle scattering. It appears to yield a controlled small coupling expansion even at asymptotically high energies where instanton methods fail. (Contribution to proceedings for Sintra '94 NATO Workshop on Electroweak Physics and the Early Universe)