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

## TL;DR

This paper explores alternative numerical stochastic perturbation methods, including Instantaneous Stochastic Perturbation Theory and Generalized Hybrid Molecular Dynamics, to overcome limitations of standard Langevin-based algorithms in $\

## Contribution

It introduces and evaluates new stochastic perturbation techniques for $\

## Key findings

- Instantaneous Stochastic Perturbation Theory shows promise
- Generalized Hybrid Molecular Dynamics is feasible for $\
- Standard Langevin methods have notable limitations

## Abstract

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. The viability of these methods is investigated in $\varphi^4$ theory.