The realization of Bose-Einstein condensation under grand canonical conditions has provided the experimental evidence for the simultaneous occurrence of macroscopic fluctuations and phase coherence of the condensate. The observation of these two features, against a consolidated tradition which wants the fluctuations to be pathological (grand canonical catastrophe) and incompatible with spontaneous symmetry breaking, calls for a comprehensive rethinking of the approach to the problem. In this paper we consider the uniform ideal gas in a box and we present an alternative conceptual framework. We show that the usually employed Bogoliubov quasiaverage construction fails to reproduce the broken-symmetry state. The observed features are accounted for by a different pattern of spontaneous symmetry breaking, characterized by the condensation of fluctuations and long-range correlations of the order parameter.

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• Bose-Einstein condensates