Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 305 / 1 / a

In the mode expansion of a Dirac field, $b^s(p)$ is the fermionic annihilation operator for a particle of four-momentum $p$ and spin angular momentum label $s$, while $d^{s†}(p)$ is the fermionic creation operator for the corresponding antiparticle. The Dirac spinor $u^s(p)$ is the positive-frequency particle wavefunction and $v^s(p)$ is the negative-frequency antiparticle wavefunction; they solve $(/p-m)u^s=0$ and $(/p+m)v^s=0$, respectively.