Improved Hamiltonian for Minkowski Yang-Mills Theory

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.

Comments: Latex, 33 pages plus 2 .epsi figures included with psfig. Revised to include new data which weakens some original conclusions