  We describe non-relativistic fermions on the lattice (Hubbard model) in the
canonical formulation using transfer matrices in fixed fermion number sectors
such that the partition function becomes fully factorized in time. By
analytically integrating out the auxiliary Hubbard-Stratanovich field due to
the four-fermion interaction, we express the system in terms of discrete, local
fermion occupation numbers which are the only remaining degrees of freedom. We
show the close relation to the fermion loop and the fermion bag formulation.
One can prove that in 1+1 dimension the fermion sign problem is absent.
Finally, we construct improved estimators for the ground state energy, 2-point
functions, and for the chemical potential.
