# Exploring the Unstable Modes Dynamics by the Lattice Schrodinger Functional

## TL;DR

This paper investigates the dynamics of unstable modes in SU(2) lattice gauge theory using a gauge-invariant effective action, revealing behavior consistent with the presence of these modes in large lattices.

## Contribution

It introduces a gauge-invariant effective action approach to analyze unstable modes in lattice gauge theory and demonstrates their behavior through numerical simulations.

## Key findings

- Unstable modes are detectable in large lattice simulations.
- Effective action density indicates the presence of unstable modes.
- Behavior depends on lattice size exceeding a critical length.

## Abstract

We analyze the problem of the Nielsen-Olesen unstable modes in the $SU(2)$ lattice gauge theory by means of a recently introduced gauge-invariant effective action. We perform numerical simulations in the case of a constant Abelian chromomagnetic field. We find that for lattice sizes above a certain critical length the density of effective action shows a behaviour compatible with the presence of the unstable modes.