Using singular classical solutions for calculating multiparticle cross sections in field theory

A method for reducing the problem of calculating multiparticle tree cross sections in $\varphi^4$ theory to the solution of a singular classical Euclidean boundary-value problem is introduced. The solutions are obtained numerically in terms of the spherical harmonic decomposition, and the corresponding estimates of the tree cross sections are found at arbitrary energies. Numerical analysis agrees with analytic results obtained earlier in the limiting cases of high and low energies.