Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 301 / 3 / a / i / Solution

The classical equations areFor any time-ordered functional $\mathcal{O}$, the three Schwinger-Dyson equations state that insertion of each left-hand side equals the corresponding contact terms obtained by $-i$ times the functional derivative of $\mathcal{O}$ with respect to $phi$, $\bar{\psi }$, or $\psi$, with the usual reversed order and Grassmann signs for fermionic derivatives.