# Fluctuation Operators and Spontaneous Symmetry Breaking

March 13, 2000

We develop an alternative approach to this field, which was to a large extent
developed by Verbeure et al. It is meant to complement their approach, which is
largely based on a non-commutative 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 $l\geq
3$ 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 developement 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.

Keywords:

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