When calculating a path integral, if the Lagrangian is quadratic in the field, then you can perform the path integral by just substituting in the classical solution for the field.(adsbygoogle = window.adsbygoogle || []).push({});

So if you have free-field Lagrangians for electrons and photons, and add the standard QED interaction term - which is linear in the electromagnetic potential [tex]j^\mu A_\mu[/tex] - then can you in principle solve the path integral by plugging in the classical solution for [tex]A_\mu[/tex]? When you do this, all [tex]A_\mu[/tex]'s disappear from your Z[J(x)] functional. You still have to perform the path integral for the fermion terms, but the photon terms are out of the path integral now.

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# Path integrals in QED

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