Optimised Renormalisation Group Flows

Exact renormalisation group (ERG) flows interpolate between a microscopic or classical theory and the corresponding macroscopic or quantum effective theory. For most problems of physical interest, the efficiency of the ERG is constrained due to unavoidable approximations. Approximate solutions of ERG flows depend spuriously on the regularisation scheme which is determined by a regulator function. This is similar to the spurious dependence on the ultraviolet regularisation known from perturbative QCD. Providing a good control over approximated ERG flows is at the root for reliable physical predictions. We explain why the convergence of approximate solutions towards the physical theory is optimised by appropriate choices of the regulator. We study specific optimised regulators for bosonic and fermionic fields and compare the optimised ERG flows with generic ones. This is done up to second order in the derivative expansion at both vanishing and non-vanishing temperature. An optimised flow for a ``proper-time renormalisation group'' is also provided to leading order in the derivative expansion.