Past exam of the advanced quantum field theory for particle physics course of the University of Oxford / 2020 / 1 / ii / Solution

The Clifford algebra of the gamma matrices gives ${\gamma }^{\nu }{\gamma }^{\mu }=2g^{\nu \mu }-{\gamma }^{\mu }{\gamma }^{\nu }$ and ${\gamma }^{\nu }{\gamma }_{\nu }=D1$. ThereforeThe contraction $g^{\nu }{}_{\nu }=D$ must be retained until the dimensional regularization calculation is complete; replacing it prematurely by four can change finite terms multiplying a ultraviolet pole.