  We study possibility of improving staggered fermions using various fat links
in order to reduce perturbative corrections to the gauge-invariant staggered
fermion operators. We prove five theorems on SU(3) projection, triviality in
renormalization, multiple SU(3) projections, uniqueness and equivalence. As a
result of these theorems, we show that, at one loop level, the renormalization
of staggered fermion operators is identical between SU(3) projected Fat7 links
and hypercubic links, as long as the action and operators are constructed by
imposing the same perturbative improvement condition. In addition, we propose a
new view of SU(3) projection as a tool of tadpole improvement for the staggered
fermion doublers. As a conclusion, we present alternative choices of
constructing fat links to improve the staggered fermion action and operators,
which deserve further investigation.
