Mode expansion of a Dirac field
= Mode expansion of a Dirac field
The mode expansion of a free Dirac field decomposes it into positive-frequency particle modes and negative-frequency antiparticle modes:
$$
\psi(x)=\sum_s\int d\Pi_p\left[b^s(p)u^s(p)e^{-ip\cdot x}+d^{s\dagger}(p)v^s(p)e^{ip\cdot x}\right].
$$
The operators $b^s$ and $d^s$ obey fermionic anticommutation relations.