We present a construction of fermionic operators in 3+1 dimensions in
terms of bosonic fields in the framework of QED(4). The basic bosonic
variables are the electric fields E(i) and their conjugate momenta A(i
). Our construction generalizes the analogous constuction of fermionic
operators in 2+1 dimensions. Loosely speaking, a fermionic operator i
s represented as a product of an operator that creates a pointlike cha
rge and an operator that creates an infinitesimal 't Hooft loop of hal
f integer strength. We also show how the axial U(1) transformations ar
e realized in this construction.