A variation of the Zamolodchikov-Faddeev algebra over a finite dimensional Hilbert space $\mathcal{ H}$ and an involutive unitary $R$-Matrix $S$ is studied. This algebra carries a natural vacuum state, and the corresponding Fock representation spaces $\mathcal{ F}_S(\mathcal{ H})$ are shown to satisfy $\mathcal{ F}_{ S\boxplus R}(\mathcal{ H}\oplus\mathcal{ K}) \cong \mathcal{ F}_S(\mathcal{ H})\otimes \mathcal{ F}_R(\mathcal{ K})$, where $S\boxplus R$ is the box-sum of $S$ (on $\mathcal{ H}\otimes\mathcal{ H}$) and $R$ (on $\mathcal{ K}\otimes\mathcal{ K}$). This analysis generalises the well-known structure of Bose/Fermi Fock spaces and a recent result of Pennig.\par It is also discussed to which extent the Fock representation depends on the underlying $R$-matrix, and applications to quantum field theory (scaling limits of integrable models) are sketched.
Categories: math-ph math.MP