We show an efficient way to compute wide-angle or all-sky statistics of galaxy intrinsic alignment in three-dimensional configuration space. For this purpose, we expand the two-point correlation function using a newly introduced spin-dependent tripolar spherical harmonic basis. Therefore, the angular dependences on the two line-of-sight (LOS) directions pointing to each pair of objects, which are degenerate with each other in the conventional analysis under the small-angle or plane-parallel (PP) approximation, are unambiguously decomposed. By means of this, we, for the first time, compute the wide-angle auto and cross correlations between intrinsic ellipticities, number densities and velocities of galaxies, and compare them with the PP-limit results. For the ellipticity-ellipticity and density-ellipticity correlations, we find more than $10%$ deviation from the PP-limit results if the opening angle between two LOS directions exceeds $30^circ - 50^circ$. It is also shown that even if the PP-limit result is strictly zero, the non-vanishing correlation is obtained over the various scales, arising purely from the curved-sky effects. Our results indicate the importance of the data analysis not relying on the PP approximation in order to determine the cosmological parameters more precisely and/or find new physics via ongoing and forthcoming wide-angle galaxy surveys.
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