  We formulate a theory to the 2D Hubbard model in a framework free of finite
size effect and numerical analytical continuation, yet containing the essential
features of the 2D Hubbard model, i.e., the correct atomic limit for large
frequencies and 2D spin fluctuations. As temperature is decreased for a 2D
half-filled band, 2D critical fluctuations give rise to a strong local maximum
in the scattering rates at the chemical potential leading to a split peak in
the spectral function. As U is increased, four peaks associated with
antiferromagnetic and Hubbard bands begin to develop in small and intermediate
frequency regimes.
