Improved Hamiltonian for Minkowski Yang-Mills Theory

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). 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 5σ, 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.