= Solution
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 $d^{s\dagger}(p)$ 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 $(\not p-m)u^s=0$ and $(\not p+m)v^s=0$, respectively.
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