Goldstone theorem at finite temperature and density

A simple proof of the thermal Goldstone theorem is given which is independent of any of the technical devices usually used to incorporate the Kubo-Martin-Schwinger condition into relativistic thermal field theories. A thermal version of the Schwinger action principle is pointed out as a means of obtaining Ward-Takahashi identities under the same general circumstances. These results may be suggestive of alternative approaches to real-time thermal field theories