2025 (source code)

= 2025
{scope}
{title2=A15272H1}

Source PDF: https://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 \i[corrected]; no claim about the contents of an earlier version is needed. Use <natural units>, the <Minkowski metric> $g=\operatorname{diag}(1,-1,-1,-1)$, and $\Box=\partial_\mu\partial^\mu$ for the <d'Alembert operator>. In question 2, every denominator has its <Feynman i-epsilon prescription> $+i0$, and $\int_k=\mu_R^{2\epsilon}\int d^{4-2\epsilon}k/(2\pi)^{4-2\epsilon}$. Here $\epsilon$ 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.