Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 304 / 1 / a

For a scalar field with classical action $S[\varphi ]$, the Euclidean source convention used throughout this question givesThe generating functional produces correlation functions through functional derivatives. For example,More generally, each derivative brings down $-\varphi /\hslash$, so an $n$-point function carries $(-\hslash {)}^n/Z[0]$.