Second quantization
= Second quantization
{title2=$\hat\psi(x)=\sum_\alpha\varphi_\alpha(x)a_\alpha$}
{wiki}
Second quantization describes identical-particle <quantum states> in <Fock space> using <creation operators> and <annihilation operators>. Relative to an <orthonormal basis> of <one-particle states>, a one-body operator becomes $\sum_{\alpha\beta}h_{\alpha\beta}a_\alpha^\dagger a_\beta$. The <canonical commutation relation> implements <bosonic> statistics, while the <canonical anticommutation relations> implement <fermionic> statistics. Expanding the <quantized field> in a complete basis gives a delta-function equal-time bracket; restricting the expansion to finitely many modes replaces that delta function by the corresponding <projection operator> kernel.