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)