Fermionic time ordering ($T[A(x)B(y)]=\theta (x^0-y^0)A(x)B(y)-\theta (y^0-x^0)B(y)A(x)$)

For two odd fermionic operators, time ordering contributes a minus sign whenever the chronological rearrangement exchanges them. For several fields the sign is the sign of a permutation restricted to the odd fields. This convention makes the free Dirac propagator a Green function of the Dirac equation with its contact term fixed by the canonical anticommutation relations.