Canonical formulation of fermionic quantum field theories on the lattice

In this talk I am going to discuss generic quantum field theories with fermionic degrees of freedom regularized on the lattice and in the canonical formulation. I will explicitly construct the transfer matrices in fixed fermion number sectors and thereby provide a complete factorization of the fermion determinant along the imaginary time. I will also discuss the relation of the canonical formulation to the fermion loop and worldline formulation. In order to illustrate the generic construction I will apply it to the Hubbard model, the Schwinger model, and QCD in the heavy-dense limit, and, in each case, comment on the corresponding solution to the fermion sign problem at finite density. As a particular physics application I will discuss finite volume particle scattering in the Schwinger model.