From Chaos to Coherence: Solving the n-Body Problem in Hyperspherical Phase Space

I present a novel solution to the (n)-body problem based on coherent SU(2) phase dynamics defined over a compact 3-sphere. Unlike the classical gravitational (n)-body formulation, which lacks general analytic solutions and exhibits chaotic behavior, the proposed framework yields discrete, stable, and fully classifiable configurations. Each "body" is represented by a topological excitation in the SU(2) phase field, decomposed into a finite set of orthonormal spectral modes of the Laplacian on (S3). I prove that for any integer (n), a stable configuration of (n) mutually orthogonal modes exists, provided the total phase density remains below a critical threshold. These solutions are characterized by quantized energy levels, spectral degeneracy, and topological coherence. The absence of singularities or chaos, combined with the emergence of stability islands and shell-like structures, suggests potential applications in nuclear modeling, coherent fusion, and topological energy systems. This work extends previous studies of quantum behavior on the 3-sphere and offers a new geometric foundation for many-body dynamics rooted in group theory and global topology.