  Large sets of baryon interpolating field operators are developed for use in
lattice QCD studies of baryons with zero momentum. Operators are classified
according to the double-valued irreducible representations of the octahedral
group. At first, three-quark smeared, local operators are constructed for each
isospin and strangeness and they are classified according to their symmetry
with respect to exchange of Dirac indices. Nonlocal baryon operators are
formulated in a second step as direct products of the spinor structures of
smeared, local operators together with gauge-covariant lattice displacements of
one or more of the smeared quark fields. Linear combinations of direct products
of spinorial and spatial irreducible representations are then formed with
appropriate Clebsch-Gordan coefficients of the octahedral group. The
construction attempts to maintain maximal overlap with the continuum SU(2)
group in order to provide a physically interpretable basis. Nonlocal operators
provide direct couplings to states that have nonzero orbital angular momentum.
