Partition function (quantum field theory) - Definition

In quantum field theory, we have a generating functional, Z[J] of correlation functions and this value, called the partition function is usually expressed by something like the following functional integral:

<math>\int \mathcal{D}\phi e^{i(S[\phi]+\int d^dx J(x)\phi(x))}<math>

where S is the action functional. This is very analogous to statistical mechanics. In fact, a Wick rotation emphasizes the similarities.

Example Usage of Partition