Summary: Let \(X\) be a locally compact Polish space and \(\sigma\) a nonatomic reference measure on \(X\) (typically \(X= \mathbb{R}^d\) and \(\sigma\) is the Lebesgue measure). Let \(X^2\ni(x,y)\mapsto\mathbb{K}(x,y)\in \mathbb{C}^{2 \times 2}\) be a \(2\times2\)-matrix-valued kernel that satisfies \(\mathbb{K}^T(x,y)=\mathbb{K}(y,x)\). We say that a point process \(\mu\) in \(X\) is hafnian with correlation kernel \(\mathbb{K}(x,y)\) if, for each \(n\in\mathbb{N}\), the \(n\)th correlation function of \(\mu \) (with respect to \(\sigma^{\otimes n})\) exists and is given by \(k^{(n)}(x_1,\ldots, x_n)=\operatorname{haf} [ \mathbb{K} (x_i, x_j)]_{i, j = 1, \ldots, n} \). Here \(\operatorname{haf}(C)\) denotes the hafnian of a symmetric matrix \(C\). Hafnian point processes include permanental and 2-permanental point processes as special cases. A Cox process \(\Pi_R\) is a Poisson point process in \(X\) with random intensity \(R(x)\). Let \(G(x)\) be a complex Gaussian field on \(X\) satisfying \(\int_{\Delta}\mathbb{E}(|G(x) |^2)\sigma(dx)<\infty\) for each compact \(\Delta\subset X\). Then the Cox process \(\Pi_R\) with \(R(x)=|G(x) |^2\) is a hafnian point process. The main result of the paper is that each such process \(\Pi_R\) is the joint spectral measure of a rigorously defined particle density of a representation of the canonical commutation relations (CCRs), in a symmetric Fock space, for which the corresponding vacuum state on the CCR algebra is quasi-free.