Phase Correlations in Non-Gaussian Fields

A breakthrough in understanding the phase information of Fourier modes in non-Gaussian fields is presented, discovering the general relation between phase correlations and the hierarchy of polyspectra. Although the exact relations involve the expansions of infinite series, one can truncate these expansions in weakly non-Gaussian fields. The phase sum, $\theta_{\sbfm{k}_1} + >... + \theta_{\sbfm{k}_N}$, satisfying $\bfm{k}_1 + ... + \bfm{k}_N = 0$, is found to be non-uniformly distributed in non-Gaussian fields, and the non-uniformness is represented by the polyspectra. A numerical demonstration proves that the distribution of the phase sum is the robust estimator of the non-Gaussianity.