Quantum mechanics is traditionally formulated on complex Hilbert spaces, while geometric structures are introduced only after the quantum formalism has been established. In this work, we investigate a coherence-geometric reformulation in which geometry is fundamental and Hilbert space emerges as a derived structure. The framework is based on a coherence manifold with local coordinates , where denotes radial coherence and denotes holonomy phase. The wavefunction arises naturally as , and the continuity equation, quantum Hamilton–Jacobi equation, and Schrödinger equation emerge from the differential geometry of the coherence manifold. A second ingredient is a discrete coherence spectrum characterized by quadruples . These integers are interpreted as coherence quantum numbers rather than phenomenological fitting parameters. The resulting framework introduces a coherence operator whose spectrum is determined by a rank-four coherence lattice. We further propose a Coherence Resonance Condition in which stable particle states correspond to rational phase locking between local coherence oscillations and global holonomy cycles. The framework combines concepts from geometric quantum mechanics, geometric quantization, Berry holonomies, Yang–Mills gauge theory, spectral geometry, and representation theory within a common geometric language.
Publication Date: 2026-06-13