The usual manifestly conserved expansions of current densities on the light cone do not lead to the correct commutation relations at equal times or on a lightlike plane. Therefore a piece must be added which is compatible with current conservation only for a specific light-cone singularity, namely, ${(z^2-i\epsilon z_0)}^{-1\mathrm{}}$, which obeys ${\square }^{\mathrm{}\left(z\right)\mathrm{}}{(z^2-i\epsilon z_0)}^{-1\mathrm{}}=0\mathrm{}$. A close relation exists between such a nonmanifestly conserved addition to the operator expansion and the well-known phenomenon of a noncausal part in the invariant function of the matrix element between one-particle states.

• Received 27 March 1972

DOI:https://doi.org/10.1103/PhysRevD.6.1670