To be used in future
 Section 5.10: Time-ordered Perturbation Theory Up Chapter 5: Path Integrals Section 5.12: Perturbation theory for the ground state energy 

5.11 Partition sum

We can express the partition sum of statistical mechanics,
in terms of a propagator: Since , we find that we can write We no introduce the Wick rotation This takes the Minkowski metric to the Euclidean metric This also changes the integral in the top of the path integral Note the change of sign in the Euclidean action . We conclude that with and the periodic boundary conditions .
 Section 5.10: Time-ordered Perturbation Theory Up Chapter 5: Path Integrals Section 5.12: Perturbation theory for the ground state energy