I'm working on some application of the Schwinger-Keldysh formalism in cosmology (studying correlation function during inflation).

  1. I saw both the operator and the path integral approach, maybe something that connects the two?

  2. Moreover, do you have an intuitive idea of why this is the correct approach to non-equilibrium QFT and to QFT in curved background?

  3. From the in-in formula: \begin{equation}\langle\mathcal{O}(t)\rangle=\langle 0|\left(\mathrm{T} e^{-i \int_{\mathrm{tin}}^{t} d \tau \hat{H}_{I}(\tau)}\right)^{\dagger}\mathcal{O}(t)\left(\mathrm{T} e^{-i \int_{t_{\mathrm{in}}}^{t} d \tau \hat{H}_{I}(\tau)}\right)| 0\rangle \end{equation} how do you proceed in perturbation theory? Just expanding both exponential? In standard QFT we were expanding the exponential in $U(-\infty, +\infty)$.

  4. How come we use two different set of fields $\phi_+$ and $\phi_-$ to do computation then?


1 Answer 1


I reproduce here with adjustments my answer to a somewhat different question, and with admittedly condensed-matter bias. Still, it might be useful.

You can find more literature here: Good reading on the Keldysh formalism


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