Antisymmetrizer

In quantum mechanics, an antisymmetrizer ${\displaystyle {\mathcal {A}}}$ (also known as an antisymmetrizing operator^[1]) is a linear operator that makes a wave function of N identical fermions antisymmetric under the exchange of the coordinates of any pair of fermions. After application of ${\displaystyle {\mathcal {A}}}$ the wave function satisfies the Pauli exclusion principle. Since ${\displaystyle {\mathcal {A}}}$ is a projection operator, application of the antisymmetrizer to a wave function that is already totally antisymmetric has no effect, acting as the identity operator.