Talk:Matsubara frequency

Two sums are divergent, the given result is misleading without explanation
Sums like
 * $$\sum_{\omega_n} \ln(\beta(-i\omega_n+\xi))= \ln(\beta\xi)+\sum_{\omega_n > 0} \ln(\beta(\omega_n^2+\xi^2))$$

in the Free energy section are divergent, and the result given looks like wishful thinking. I know that the result can be derived formally by integrating around the branch cut of the logarithm, and ignoring contributions from parts of the integration path where $$|z|$$ is large. At the very least an explanation of the regularization is required. To my knowledge the only clean way to get the result is to use a path integral with discrete imaginary time steps.radical_in_all_things (talk) 20:08, 5 March 2021 (UTC)