1
$\begingroup$

Assuming that one knows Feynman rules for QFT, what is the simplest way to generalize them for $T \neq 0$ case? What is the main difference? Can we just read them off from Lagrangian the same way as in QFT?

Since the partition function $Z$ in thermal quantum field theory is just $Z_{QFT}$ with substitution $t \rightarrow i\tau$, with $\tau$ being integrated from $0$ to $\beta$, as opposed to time $t$ being integrated from $-\infty$ to $\infty$, and with different boundary conditions for the fields (periodic/anti-periodic for bosons/fermions), can we use the same analogy for the generalization of the Feynman rules?

$\endgroup$
1
$\begingroup$

Finite temperature Feynman rules are simply zero temperature Feynman rules for Euclidean ($t\to i\tau$) QFT in periodic imaginary time. So instead of continuous values for the momenta, you will have a discrete spectrum for the timelike moments (such as in the infinite potential well in basic quantum mechanics). It's called the Matsubara formalism, if you want to google for more.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.