Fermionic operators from bosonic fields in 3+1 dimensions

We present a construction of fermionic operators in 3+1 dimensions in terms of bosonic fields in the framework of QED4. The basic bosonic variables are the electric fields Ei and their conjugate momenta Ai. Our construction generalizes the analogous constuction of fermionic operators in 2+1 dimensions. Loosely speaking, a fermionic operator is represented as a product of an operator that creates a pointlike charge and an operator that creates an infinitesimal ʹt Hooft loop of half integer strength. We also show how the axial U(1) transformations are realized in this construction.