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I'm a junior learner of QFT, and I wonder if I can add a classical approximated potential (like Coulomb potential) to a total interaction \begin{equation}V=V_{\mathrm{Coulomb}}+V_{\mathrm{internal}} \end{equation} Where $V_{\mathrm{internal}}$ is calculated by \begin{equation}V_{\mathrm{internal}}=\int{H(x)d^3x}\end{equation} Therefore the $S$ matrix is \begin{equation}S=T \exp \left [-i\int_{-\infty}^{\infty}{dt} {V_{\mathrm{internal}}(t)}+{V_{\mathrm{external}}(-t)} \right]\end{equation} $V_{\mathrm{external}}(-t)$ is to suppose the external field doesn't change by time so I reversed the time evolution picture. The $S$ matrix can still be expanded by Dyson series. So during a collison reaction, like electron postrion annihilation in solid, can I add the external potential accroding to the DFT to the Dyson series to make a correction of $S$-matrix? Indeed it's a violation of unitrary of $S$ matrix, but still, can it be applied as a perturbation?

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  • $\begingroup$ Please some one help me $\endgroup$ – Mmmao Oct 1 at 10:53
  • $\begingroup$ Please someone help me $\endgroup$ – Mmmao Oct 3 at 5:00
  • $\begingroup$ Why won’t someone help me $\endgroup$ – Mmmao Oct 3 at 6:44

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