In four dimensions, $[\psi]=3/2$, $[A_\mu]=1$, and $[F_{\mu\nu}]=2$. The minimal-coupling operator $\bar\psi\gamma^\mu A_\mu\psi$ has dimension four, so $[e]=0$ and $e$ is a <marginal coupling>. The <Pauli term> $\bar\psi[\gamma^\mu,\gamma^\nu]F_{\mu\nu}\psi$ has dimension five, so $[\lambda]=-1$ and $\lambda$ is an <irrelevant coupling> by <power counting in quantum field theory>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 301 / 1 / a / Solution

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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-301/1/a/solution