Monte Carlo computation of the spectral density function in the interacting scalar field theory

We study the phi(4) field theory in d = 4. Using bold diagrammatic Monte Carlo method, we solve the Schwinger-Dyson equations and find the spectral density function of the theory beyond the weak coupling regime. We then compare our result with the one obtained from the perturbation theory. At the end, we utilize our Monte Carlo result to find the vertex function as the basis for the computation of the physical scattering amplitudes.