  We study the Ward identity for the effective photon-electron vertex summing
the ladder diagrams contributing to the electrical conductivity in hot QED at
leading logarithmic order. It is shown that the Ward identity requires the
inclusion of a new diagram in the integral equation for the vertex that has not
been considered before. The real part of this diagram is subleading and
therefore the final expressions for the electrical conductivity at leading
logarithmic order are not affected.
