In four spacetime dimensions the action is dimensionless, so the <mass dimension> of the Lagrangian density is $[\mathcal L]=4$. The kinetic term gives $[\phi]=1$, and $g\phi^3$ then gives
$$
[g]=4-3[\phi]=1.
$$
Thus $g$ has mass dimension one and is a <relevant coupling> under <power counting in quantum field theory>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 301 / 2 / a / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/iii/paper-301/2/a/solution