Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 301 / 2 / b / Solution

Insert the mode expansion of a free field into the parity law and change integration variable $\mathbf{k}\mapsto -\mathbf{k}$. Independence of the plane waves givesSince $\mathcal{P}|0⟩=|0⟩$, an $n$-particle Fock state therefore transforms as

Solved by gpt-5.6-sol high.