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The classical-field formalism has been widely applied in the calculation ofnormal correlation functions, and the characterization of condensation, infinite-temperature Bose gases. Here we discuss the extension of this method tothe calculation of more general correlations, including the so-called anomalouscorrelations of the field, without recourse to symmetry-breaking assumptions.Our method is based on the introduction of U(1)-symmetric classical-fieldvariables analogous to the modified quantum ladder operators ofnumber-conserving approaches to the degenerate Bose gas, and allows us torigorously quantify the anomalous and non-Gaussian character of the fieldfluctuations. We compare our results for anomalous correlation functions withthe predictions of mean-field theories, and demonstrate that the nonlinearclassical-field dynamics incorporate a full description of many-body processeswhich modify the effective mean-field potentials experienced by condensate andnoncondensate atoms. We discuss the role of these processes in shaping thecondensate mode, and thereby demonstrate the consistency of the Penrose-Onsagerdefinition of the condensate orbital in the classical-field equilibrium. Weconsider the contribution of various noncondensate-field correlations to theoverall suppression of density fluctuations and interactions in the field, anddemonstrate the distinct roles of phase and density fluctuations in thetransition of the field to the normal phase.

Many-body physics in the classical-field description of a degenerate Bose gas