00-111 Requardt, M.

Fluctuation Operators and Spontaneous Symmetry Breaking (63K, LATeX 2e) Mar 14, 00

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Abstract. In the following we develop an in various respects new approach to this field, which was to a large extent developed by Verbeure et al. and which may complement their approach, which is largely based on a non-commutative central limit theorem. 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.

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