 Weyl ordering

Weyl ordering symmetrizes position and momentum factors in a classical polynomial before promoting them to an operator. Its phase-space symbol corresponds to midpoint time slicing of a phase-space path integral. In particular, the Weyl symbol of $a^{†}a$ is $\bar{\psi }\psi -1/2$, whereas its normal ordering symbol is $\bar{\psi }\psi$.