  The distribution of the characteristic polynomial $Z(U,\theta)$ of $N\times
N$ matrices $U$ in the Circular Unitary Ensemble is studied by the method of
second quantization for one-dimensional fermions. For infinite $N$ the Gaussian
distribution of $Z(U,\theta)$ is established straightforwardly by bosonization.
A general expression for the $n$-point correlation function of the
characteristic polynomial at different points is given by this method. The case
of finite $N$ is discussed.
