The engineering value follows from the Gaussian kinetic term. At an interacting <renormalization-group fixed point>, momentum-dependent self-energy diagrams change the kinetic coefficient, and restoring its normalization requires <wave-function renormalization>. The resulting <anomalous dimension> $\eta$ changes the full <scaling dimension> to
$$
\boxed{\Delta_\phi=\frac{d-2+\eta}{2}}.
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 303 / 2 / c / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/iii/paper-303/2/c/solution