Fock-Space Projector Studied in Weyl Ordering Approach

We find that the Fock space projector |n〉〈n| is a Weyl ordered Laguerre polynomial \(2{\,}^{:}_{:}(-)^{n}L_{n} ( 4a^{\dagger}a ) e^{-2a^{\dagger}a}{\,}^{:}_{:}\), where a † a is the number operator\(,{}^{:}_{:}\ {}^{:}_{:}\) denotes the Weyl ordering symbol. This brings convenience to derive the Wigner functions of many other quantum states.