- #1
RedX
- 970
- 3
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.
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.
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.