 2025

Source PDF: mmathphys.physics.ox.ac.uk/sites/g/files/vzsiac2991/files/mmathphys/documents/media/a15272h1corrected.pdf

Solutions to all seventeen lettered parts. The source is the version publicly labelled corrected; no claim about the contents of an earlier version is needed. Use natural units, the Minkowski metric $g=\mathrm{diag}(1,-1,-1,-1)$, and $\square ={\partial }_{\mu }{\partial }^{\mu }$ for the d'Alembert operator. In question 2, every denominator has its Feynman i-epsilon prescription $+i0$, and ${\int }_k={\mu }_R^{2ϵ}\int d^{4-2ϵ}k/(2\pi {)}^{4-2ϵ}$. Here $ϵ$ is the dimensional regularization parameter; the small parameter in 1(f) is denoted $\eta$ to distinguish it. Signs follow the insertion Feynman rules printed on source page 4.