denote the left creation operator, defined by $\ell(h)\Omega = h$ and $\ell(h)(h_1 \otimes \cdots \otimes h_m) = h \otimes h_1 \otimes \cdots \otimes h_m$ for $m \geq 1$. Let $\varphi: \mathcal{L}(\mathcal{F}(H)) \to \mathbb{C}$ be the vacuum vector state