A Renormalizable Quantum Gravity Theory Based on the Coupling of Global Unified Wave Field and Spacetime Background Field

To resolve the fundamental incompatibility between general relativity and quantum field theory at the Planck scale, the non-renormalizable dilemma of traditional quantum gravity, and the lack of direct observational evidence for the dark matter hypothesis, this paper constructs a novel quantum gravity theory with a coupling framework of global unified wave field and spacetime background field. Starting from the first principles, this study completes the physical interpretation and rigorous mathematical derivation of Lagrangian density, step-by-step deduction of coupled interaction terms, and derivation of gravitational field equations based on the principle of least action. Following the standard paradigm of particle physics, a systematic framework including gauge group structure, vacuum expectation value and spontaneous symmetry breaking evolution is established, and the natural derivation of various interaction coupling terms is realized. This paper carries out complete series calculations of high-energy quantum field theory, including the construction of one-loop and two-loop Feynman topologies, four-dimensional momentum integral, ultraviolet divergence separation, algebraic derivation of minimal subtraction scheme, analytical solution of beta function and renormalization group running analysis at different energy scales. Dynamical equations for the Bullet Cluster collision are established to implement numerical calculation of velocity offset, point-to-point fitting between gravitational potential and visible matter distribution, and residual error verification. The theoretical results achieve satisfactory quantitative matching with astronomical observations within a reasonable deviation range. Rather than an empirical patch for modified gravity frameworks, this model represents a fundamental paradigm reconstruction of physical laws. It can satisfy various cosmological observational constraints self-consistently and overcome the common theoretical defects of existing dark matter alternatives. Systematic self-checks including dimensional consistency verification, multi-scale energy scope definition, parameter physical interpretation and causal locality analysis are accomplished. Compared with string theory and loop quantum gravity, the present theory possesses remarkable structural advantages, forming a logically closed, mathematically complete and observationally consistent original quantum gravity framework.