satisfy $$h_1 \wedge \cdots \wedge h_i \wedge \cdots \wedge h_j \wedge \cdots \wedge h_m
     \equals - h_1 \wedge \cdots \wedge h_j \wedge \cdots \wedge h_i \wedge \cdots \wedge h_m$$ for $1\le i < j \le m$. In the context of $n$-electron systems, wedge products are usually called “Slater determinants." The inner product of two Slater determinants is $$\langle h_1 \wedge \cdots \wedge h_{m} ,\ h'_1 \wedge \cdots \wedge h'_m \rangle
        \equals
        \det \big( \langle h_i, h'_j \rangle \big)_{ij=1}^{\ m}\ .$$ This extends to an inner product on the linear span of the Slater determinants, and the completion of this linear span is the Hilbert space $\wedge^m \HH$.

Let $\BB(\FFF)$ denote the space of bounded operators on $\FFF = \FFF(\HH)$. Creation and annihilation operators $\hat{a}^*(h)$ and $\hat{a}(h)$ on $\FFF$ may be defined for each $h \in \HH$ as in Refs. [@BratteliRobinson; @AlickiFannes]. These creation and annihilation operators (creators and annihilators) are bounded operators that satisfy the canonical anticommutation relations and generate the Fock representation of the CAR algebra. This is the uniform-norm closure in $\BB(\FFF)$ of the algebra of polynomials in the creators and annihilators. We shall denote the CAR algebra over $\HH$ by $\mathfrak{A}(\HH)$ and its Fock representation as a 