Transfer matrix and nonperturbative renormalization of fermionic currents in lattice QCD

The functional integral representation for fermionic observables on the lattice is studied. In particular, Grassmannian representations of the scalar $\hatJ^{(S)}$ and pseudoscalar $\hatJ^{(P)}$ currents and pseudoscalar correlator are derived. It is also discussed the connection between the fermionic Fock space and boundary conditions along the time direction.