Coincident-point bunching factors ($g^{(n)}(0)=n!$)

A single-component chaotic Gaussian bosonic field has normalized coincident normally ordered correlation $n!$: every pairing contributes the same product of densities. A same-component fermionic field instead has zero coincident correlations for $n\ge 2$ by exclusion. These are state-dependent statements: a coherent bosonic field has factor one, and a single-mode number state has $N^{\underline{n}}/N^n$. Ratios to distant unnormalized correlations additionally require the compared densities to agree and distant correlations to factorize.