 00111 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 noncommutative 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 energymomentum 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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