Improved Hamiltonian for Minkowski Yang-Mills theory

I develop an improved Hamiltonian for classical, Minkowski Yang-Mills theory, which evolves infrared fields with tree level corrections from lattice spacing a beginning at O(a⁴). I use it to investigate the response of Chern-Simons number to a chemical potential, and to compute the maximal Lyapunov exponent. The Lyapunov exponent has a small a limit, and the Chern-Simons number response appears to be approaching one at the finest lattices considered. In both cases the limit is within 10% of the limit found using the unimproved (Kogut-Susskind) Hamiltonian. For the maximal Lyapunov exponent the limits differ between Hamiltonians by about 5%, significant at about 5σ, indicating that while a small a limit exists, its value depends on the specifics of the lattice cutoff. For Chern-Simons number the difference between Hamiltonians is within statistical errors of about 10%, which constitutes an upper bound on the lattice regulation dependence.