Charge dependence of operators in QED renormalization - Physics Stack Exchange most recent 30 from physics.stackexchange.com 2019-07-19T10:17:33Z https://physics.stackexchange.com/feeds/question/153283 http://www.creativecommons.org/licenses/by-sa/3.0/rdf https://physics.stackexchange.com/q/153283 1 Charge dependence of operators in QED renormalization FenderLesPaul https://physics.stackexchange.com/users/53077 2014-12-14T19:31:36Z 2014-12-14T19:31:36Z <p>Consider a UV cutoff regulator $\Lambda$ with an effective QED lagrangian: $\mathcal{L}_{\Lambda} = \bar{\psi}_{\Lambda}(i\not \partial - m_{\Lambda})\psi_{\Lambda} - \frac{1}{4}(F^{\mu\nu}_{\Lambda})^2 - e_{\Lambda}\bar{\psi}_{\Lambda}\not A_{\Lambda}\psi_{\Lambda}$. One can of course add more local operators to $\mathcal{L}_{\Lambda}$ by considering corrections from various 1-loop diagrams of the full theory. The $\Lambda$ dependence of these 1-loop corrections is easy to determine from the dimension of the operator. But how does one systematically go about determining the dependence on the bare charge $e$ of the 1-loop corrections given the operators? For example, if I have the operator $\bar{\psi}(\partial^2 F^{\mu\nu})\sigma_{\mu\nu}\psi$ or the operator $\bar{\psi}\partial_{\mu}F^{\mu\nu}\gamma_{\nu}\psi$ or even $\bar{\psi}\not D^3 \psi$ (which are allowed by the theory since they respect gauge invariance, Lorentz invariance, and parity) how can I tell how the associated 1-loop correction will depend on $e$?</p> <p>One obvious thing to do would be to try and construct the 1-loop Feynman diagrams that these operators are generated by in the full theory and get the $e$ dependence by looking at the number of vertices but I do not have a good enough intuition to do this. For example what Feynman diagrams would generate the three operators above? Thanks in advance!</p>