  We construct a Fock space associated to a symmetric function $Q:U\times U \to
(-1,1)$, where $U$ is a nonempty open subset of $\mathbb R^j$ for some $j$.
Namely, we will have operator-valued distributions $a(x)$ and $a^+(y)$
satisfying $a(x)a^+(y)-Q(x,y)a^+(y)a(x)=\delta(x-y)$. Analogous to the
$q_{ij}$-Fock space of Bozejko and Speicher, we have field operators arising as
the sum of the creation and annihilation operators. These operators generate a
von Neumann algebra analogous to the free group factors, and we will show that
they are factors which do not have property $\Gamma$. It was pointed out to us
by an anonymous referee that this is a special case of a theorem of Krolak.
