# Improved Hamiltonian for Minkowski Yang-Mills Theory

## TL;DR

This paper introduces an improved Hamiltonian for Minkowski Yang-Mills theory that reduces lattice artifacts, enabling more accurate investigation of infrared field dynamics, Chern-Simons number response, and Lyapunov exponents.

## Contribution

The paper develops a higher-order corrected Hamiltonian for classical Minkowski Yang-Mills theory to minimize lattice spacing effects in simulations.

## Key findings

- The improved Hamiltonian reduces lattice artifacts to within 10% for key quantities.
- The maximal Lyapunov exponent's small $a$ limit differs by about 5%, indicating lattice effects influence its value.
- Chern-Simons number response shows potential dependence on lattice regulation, but data is inconclusive.

## Abstract

I develop an improved Hamiltonian for classical, Minkowski Yang-Mills theory, which evolves infrared fields with corrections from lattice spacing $a$ beginning at $O(a^4)$. I use it to investigate the response of Chern-Simons number to a chemical potential, and to compute the maximal Lyapunov exponent. Both quantities have small $a$ limits, in both cases within $10\% $ of the limit found using the unimproved (Kogut Susskind) Hamiltonian. For the maximal Lyapunov exponent the limits differ by about $5 \% $, significant at about $5 \sigma$, indicating that while a small $a$ limit exists, its value is corrupted by lattice artefacts. For the response of Chern-Simons number the statistics are not good enough to resolve $ 5 \% $ differences, but it seems possible in analogy with the Lyapunov exponent that the final answer depends on the lattice regulation.