Past exam of the mathematics course of the University of Cambridge / 2018 / iii / Paper 301 / 1 / i

Use $\hslash =c=1$ and the Minkowski metric $\eta =\mathrm{diag}(1,-1,-1,-1)$ throughout. In the four-component Dirac spinor representation, the gamma matrices generate the Clifford algebraThus $({\gamma }^0{)}^2=I_4$, $({\gamma }^i{)}^2=-I_4$, and matrices with distinct indices anticommute. Indices are lowered with $\eta$, so ${\gamma }_{\mu }={\eta }_{\mu \nu }{\gamma }^{\nu }$ and $/p=p_{\mu }{\gamma }^{\mu }$.