A scalar field of <scaling dimension> $\Delta_\phi$ has a scale-invariant <two-point correlation function> proportional to $|x|^{-2\Delta_\phi}$. Comparison with the stated form gives
$$
\boxed{\Delta_\phi=\frac{d-2+\eta}{2}}.
$$
The difference $\eta/2$ from the engineering value is the field's <anomalous dimension>, generated by fluctuations and interactions at a non-Gaussian <renormalization-group fixed point>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 303 / 2 / c / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-303/2/c/solution