Perturbatively exact multiparticle amplitudes from Landau method

We propose a perturbatively exact relation between scattering amplitudes in bosonic theories and vacuum-to-vacuum transition amplitudes in the same theories with vanishingly small source on a singular background. The derivation of this formula is based on the exact version of quantum-mechanical Landau method. Being applied to the amplitudes of $n \gg 1$ particle production, it resums the powers of $g^2 · n$ in the perturbative series, where g is a coupling constant, thus describing the double-scaling limit $g > 0, g^2 · n =\text{const}$. In the lowest semiclassical order, it reproduces non-perturbative Rubakov-Son-Tinyakov conjecture. We verify our new relation by explicitly computing transition amplitudes between vacuum and highly excited states of anharmonic oscillator and discuss its application to multiparticle production in the scalar $\varphi^4$ theory.