- #1
CAF123
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I am considering the ##\psi^4## interacting theory and a lagrangian of the form $$\mathcal L = \frac{1}{2}Z_{\psi} \partial^{\mu} \psi \partial_{\mu} \psi - \frac{1}{2}Z_m m^2 \psi^2 - \frac{1}{4!}Z_g g \psi^4$$ with generating functional for the interacting theory $$Z(J) = \int \mathcal D [\psi] \exp(i \int d^4 x(\mathcal L_o + \mathcal L_I + J\psi))$$ which is then written like $$\exp\left(i [\int d^4 y \frac{\delta}{i\delta J(y)} (-\frac{1}{2}(Z_{\psi}-1)\partial^2 - \frac{1}{2}(Z_m -1) m^2) \frac{\delta}{i\delta J(y)} - \frac{Z_g g}{4!}\left(\frac{\delta}{i\delta J(y)}\right)^4]\right) Z_o(J)$$
My notes then go onto say that the feynman rules can be easily deduced from this. I am wondering how so? I realize that the part in brackets between the two derivatives is like a propagator term sandwiched between two source terms and the last term is like a vertex rule, but I am not sure how to formally identify or extract the rules.
Thanks!
My notes then go onto say that the feynman rules can be easily deduced from this. I am wondering how so? I realize that the part in brackets between the two derivatives is like a propagator term sandwiched between two source terms and the last term is like a vertex rule, but I am not sure how to formally identify or extract the rules.
Thanks!