With the aim of resolving theoretical issues associated with the fourth root
prescription for dynamical staggered fermions in Lattice QCD simulations, we
consider the problem of finding a viable lattice Dirac operator D such that
(det D_{staggered})^{1/4} = det D. Working in the flavour field representation
we show that in the free field case there is a simple and natural candidate D
satisfying this relation, and we show that it has acceptable locality behavior:
exponentially local with localisation range vanishing ~ (a/m)^{1/2} for lattice
spacing a -> 0. Prospects for the interacting case are also discussed, although
we do not solve this case here.Comment: 29 pages, 2 figures; some revision and streamlining of the
discussions; results unchanged; to appear in PR