Investigation of New Methods for Numerical Stochastic Perturbation Theory in $\varphi^4$ Theory

Understand

Numerical stochastic perturbation theory is a powerful tool for estimating high-order perturbative expansions in lattice field theory.

• The standard algorithms based on the Langevin equation, however, suffer from several limitations which in practice restrict the potential of this technique.
• In this work we investigate some alternative methods which could in principle improve on the standard approach.
• In particular, we present a study of the recently proposed Instantaneous Stochastic Perturbation Theory, as well as a formulation of numerical stochastic perturbation theory based on Generalized Hybrid Molecular Dynamics algorithms.