Ward-Takahashi identity at finite temperature

The authors provide a perturbative check of Ward-Takahashi identities of QED at finite temperature using a new real time formalism, thermo field dynamics. Gauge invariance is shown to hold up to the two-loop level except one special case. In verifying the identities, a consistent rule is found in dealing with products of singular terms which are characteristic of the real time formalism. (author)