On the fourth root prescription for dynamical staggered fermions

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. The problem of gauging this operator such that the determinant relation continues to hold is not solved here (a problem for future work). However, we give arguments suggesting that the difference between the effective actions corresponding to (detD_{staggered})^{1/4} and detD for any choice of gauging of our D has the form of a lattice Yang-Mills action for the gauge field