Ψ Ψ ( x 1 , … … x n ) = 1 n ! | ψ ψ 1 ( x 1 ) ⋯ ⋯ ψ ψ n ( x 1 ) ⋮ ⋮ ⋱ ⋱ ⋮ ⋮ ψ ψ 1 ( x n ) ⋯ ⋯ ψ ψ n ( x n ) | is an antisymmetric function on X n . It can thus be naturally interpreted as an element of the n -particle sector of the odd Fock space. The normalization is chosen such that ‖ ‖ Ψ Ψ ‖ ‖ = 1 if the functions ψ ψ 1 , … … , ψ ψ n are orthonormal. There is a similar "Slater permanent" with the determinant replaced with the permanent which gives elements of n -sector of the even Fock space.