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.

中文翻译：

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ZF 代数和 R 矩阵的 Fock 表示

研究了 Zamolodchikov-Faddeev 代数在有限维 Hilbert 空间 $\mathcal{H}$ 和对合酉 $R$-矩阵 $S$ 上的变体。该代数带有自然真空状态，相应的 Fock 表示空间 $\mathcal{F}_S(\mathcal{H})$ 被证明满足 $\mathcal{F}_{S\boxplus R}(\mathcal{ H}\oplus\mathcal{K}) \cong \mathcal{F}_S(\mathcal{H})\otimes \mathcal{F}_R(\mathcal{K})$，其中 $S\boxplus R$ 是$S$（在 $\mathcal{H}\otimes\mathcal{H}$ 上）和 $R$（在 $\mathcal{K}\otimes\mathcal{K}$ 上）的框和。该分析概括了著名的 Bose/Fermi Fock 空间结构和 Pennig 的最新结果。\par 还讨论了 Fock 表示在多大程度上取决于基础 $R$-矩阵，以及在量子场论中的应用（可积模型的缩放限制）被勾画。