Partition function (quantum field theory)

In quantum field theory, the partition function ${\displaystyle Z[J]}$ is the generating functional of all correlation function, generalizing the characteristic function of probability theory.

It is usually expressed by the following functional integral:

where S is the action functional.

The partition function in quantum field theory is a special case of the mathematical partition function, and is related to the statistical partition function in statistical mechanics. The primary difference is that the countable collection of random variables seen in the definition of such simpler partition functions has been replaced by an uncountable set, thus necessitating the use of functional integrals over a field ${\displaystyle \phi }$.

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