Monte Carlo Computation of Spectral Density Function in Real-Time Scalar Field Theory

TL;DR

This paper develops a non-perturbative Monte Carlo method to compute the spectral density function in real-time scalar field theory, overcoming the sign problem and enabling analysis beyond perturbation theory.

Contribution

It introduces a novel approach combining Schwinger-Dyson equations with a new analytical integral method and Monte Carlo simulations for spectral functions in real-time quantum field theory.

Findings

Non-perturbative spectral function obtained via Monte Carlo

Comparison with perturbative results shows significant differences

Full vertex function computed for real-time scattering amplitudes

Abstract

Non-perturbative study of "real-time" field theories is difficult due to the sign problem. We use Bold Schwinger-Dyson (SD) equations to study the real-time $\phi^4$ theory in $d=4$ beyond the perturbative regime. Combining SD equations in a particular way, we derive a non-linear integral equation for the two-point function. Then we introduce a new method by which one can analytically perform the momentum part of loop integrals in this equation. The price we must pay for such simplification is to numerically solve a non-linear integral equation for the spectral density function. Using Bold diagrammatic Monte Carlo method we find non-perturbative spectral function of theory and compare it with the one obtained from perturbation theory. At the end we utilize our Monte Carlo result to find the full vertex function as the basis for the computation of real-time scattering amplitudes.