Computing the Effective Hamiltonian of Low-Energy Vacuum Gauge Fields

TL;DR

This paper introduces a lattice simulation method to rigorously compute the effective Hamiltonian of vacuum gauge fields, demonstrated by calculating the instanton size distribution in SU(2) gluon dynamics without model assumptions.

Contribution

It presents a novel, model-independent lattice approach to determine the effective Hamiltonian of vacuum gauge fields, advancing non-perturbative QCD studies.

Findings

Computed instanton size distribution in SU(2) gluon dynamics

Demonstrated the method's model independence and parameter-free nature

Provided a new tool for non-perturbative vacuum analysis

Abstract

A standard approach to investigate the non-perturbative QCD dynamics is through vacuum models which emphasize the role played by specific gauge field fluctuations, such as instantons, monopoles or vortexes. The effective Hamiltonian describing the dynamics of the low-energy degrees of freedom in such approaches is usually postulated phenomenologically, or obtained through uncontrolled approximations. In a recent paper, we have shown how lattice field theory simulations can be used to rigorously compute the effective Hamiltonian of arbitrary vacuum models by stochastically performing the path integral over all the vacuum field fluctuations which are not explicitly taken into account. In this work, we present the first illustrative application of such an approach to a gauge theory and we use it to compute the instanton size distribution in SU(2) gluon-dynamics in a fully model independent and parameter-free way.