Shadow Hamiltonians, Poisson Brackets, and Gauge Theories

Understand

Numerical lattice gauge theory computations to generate gauge field configurations including the effects of dynamical fermions are usually carried out using algorithms that require the molecular dynamics evolution of gauge fields using symplectic integrators.

• Sophisticated integrators are in common use but are hard to optimise, and force-gradient integrators show promise especially for large lattice volumes.
• We explain why symplectic integrators lead to very efficient Monte Carlo algorithms because they exactly conserve a shadow Hamiltonian.
• The shadow Hamiltonian may be expanded in terms of Poisson brackets, and can be used to optimize the integrators.