  We study the fermion sign problem in a theory of non-relativistic fermions
with a spin-independent repulsive interaction. We work in polar co-ordinates in
momentum space, which makes it straightforward to keep only the low-energy
degrees of freedom close to the Fermi surface. This is sufficient for the
purpose of calculating many physically important low-energy observables. We
find indications that the sign problem in this effective theory will be weaker
than in the full theory, so low-energy properties of the theory could be
calculated by modifying the action to make it positive semi-definite and
including reweighting factors in the observables. We discuss suitable
modifications of the action, and describe a possible lattice realization of the
polar momentum space formulation of the theory.
