Consider a system of 2 identical fermions.
$$\psi_{k_1,k_2}(x_1,x_2,m_1, m_2) = \langle x_1\,x_2\,m_1\,m_2\mid \psi \rangle$$
According to what I have read we can construct a state with the right antisymmetry properties by
$$\psi_{k_1,k_2}(x_1,x_2,m_1, m_2) =...