Correlation functions and Green functions: Zero-frequency anomalies

The zero-frequency anomaly that can arise in the Fourier transform of certain quantum mechanical correlation functions is investigated. Two physical interpretations are given to the anomalous term. It is shown that any method for calculating the thermal Green function (though not the retarded or advanced commutator Green functions) should also yield the strength of the anomaly. An example is given. A critical discussion is given of recent contributions by other authors.