Second-quantization approach to characteristic polynomials in RMT

The distribution of the characteristic polynomial Z(U, theta) of N x 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.