Under $x'=x/\zeta$ and the Gaussian field rescaling $\phi'(x')=\zeta^{(d-2)/2}\phi(x)$, a mass squared has <engineering dimension> two and a quartic coupling has dimension $4-d$. Therefore
$$
\boxed{A=2,\qquad B=4-d}.
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 303 / 3 / a / iv / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/iii/paper-303/3/a/iv/solution