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 (detDstaggered)1/4=detD. Working in the flavor 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 a localization range vanishing ~√a/m for lattice spacing a→0. Prospects for the interacting case are also discussed, although we do not solve this case here.
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David Adams (2005) studied this question.