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A three-body scattering theory previously proposed by one of the presentauthors is developed to be applied to the saturated ferromagnetic state in thetwo-dimensional Hubbard model. The single-particle Green's function iscalculated by taking account of the multiple scattering between two electronsand one hole. Several limiting cases are discussed and the relation to thevariational principle is examined. The importance of the three-body correlationis demonstrated in comparison with the results of the ladder approximation. Apossible phase boundary for the Nagaoka ground state is presented for thesquare lattice, which improves the previous variational results.Comment: 13 pages, 8 Postscript figures, submitted to Phys.Rev.

Electron Correlations in the Nagaoka State on the Square Lattice -Three-Body Correlations-