Species doubling and transfer matrices for fermionic fields

Abstract

The transfer-matrix formalism for relating Hamiltonian quantum mechanics and Euclidean path integrals is discussed in the context of fermionic fields. Particular emphasis is placed on the extra fermionic species encountered with the naive discretization of time. When both particles and antiparticles are present, the Wilson projection-operator formalism arises naturally for the temporal coordinate. We discuss in detail how the Hilbert space must be enlarged to remove these projections.