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

Under $x^{\prime }=x/\zeta$ and the Gaussian field rescaling ${\varphi }^{\prime }(x^{\prime })={\zeta }^{(d-2)/2}\varphi (x)$, a mass squared has engineering dimension two and a quartic coupling has dimension $4-d$. Therefore