# A strange partition function

1. Jan 3, 2012

### zakk87

While reading an article about superconductivity I found out a strange partition function which I don't know how to re-obtain. The partition function is given by:

$$Z=-\prod_{\omega,\mathbf{k}} (\omega^2 + E(\mathbf{k})^2)$$

where the sum over $\omega$ runs over Matsubara frequencies and $E(\mathbf{k})$ is the dispersion relation for the system.

I'm pretty sure that the procedure is quite general and does not depend upon the specific details of the the system and upon the analytical form of the dispersion relation.

P.S.: Anyone knows how to derive such a form for the partition function starting from the standard definition?