# Generating functional (or partition function)

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• #1
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## Main Question or Discussion Point

I am reading a book (Di Francesco's "CFT", pg 337) in which it is given that if we take the operator that translates the system along some direction (which is a combination of time and space) as 'A', then the partition function is just trace(A).
How do we get this?

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• #2
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Any one?

• #3
Avodyne
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I don't have that book, but the spacetime translation operator is exp(iPa), where P is the four-momentum vector operator, and a is a constant four-vector (that you are translating by). The partition function is usually Tr[exp(-beta H)]. So except for a factor of i, this is the translation operator with a translation in the time direction by beta.

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