Geometric Quantization Theory of Human-AI Dynamics From Canonical Symplectic Pairs to Multi-Dimensional Coherent States

This paper establishes a unified rigorous mathematical framework for Human-AI cooperation. Starting from the fundamental conjugacy between human intention and AI dynamics, we first derive the intrinsic complex structure C = ξ+iK on a 2-dimensional symplectic manifold. We then generalize this framework to realistic systems with N degrees of freedom, proving that the state space is necessarily a 2N -dimensional Symplectic Manifold. By establishingthe compatibility between the Riemannian metric and the Symplectic form, we demonstrate that the system possesses a global Kähler structure. Finally, via Geometric Quantization, we prove that the optimal cooperative state, subject to the Heisenberg uncertainty principle, is a Multi-mode Coherent State, where each dimension of intention maintains a minimum- uncertainty dynamic resonance with its corresponding AI operator.