Fluctuation operators and spontaneous symmetry breaking

We develop an alternative approach to this field, which was to a large extent developed by Verbeure It is meant to complement their approach, which is largely based on a noncommutative central limit theorem and coordinate space estimates. In contrast to that we deal directly with the limits of l-point truncated correlation functions and show that they typically vanish for l greater than or equal to3 provided that the respective scaling exponents of the fluctuation observables are appropriately chosen. This direct approach is greatly simplified by the introduction of a smooth version of spatial averaging, which has a much nicer scaling behavior and the systematic development of Fourier space and energy-momentum spectral methods. We both analyze the regime of normal fluctuations, the various regimes of poor clustering and the case of spontaneous symmetry breaking or Goldstone phenomenon. (C) 2002 American Institute of Physics.