A Quantum Gravity Unification Theory Based on Four U (1) Gauge Fields with Emergent Geometry: Complete Construction History and Mathematical Details

This paper proposes and completely constructs a quantum gravity unification theory based on four U (1) gauge fields. Through systematic exploration, we start from the initial linear Fierz-Pauli action and progressively solve core issues of renormalizability, unitarity, and low-energy correspondence. The core innovation of the theory lies in treating spacetime geometry as an emergent phenomenon of gauge field correlation functions, rather than a fundamental entity. We provide detailed mathematical formulation of the complete theory, including action construction, quantization scheme, renormalization procedure, unitarity proof, and low-energy limit analysis. The theory is mathematically rigorous, physically complete, and provides clear, testable predictions for quantum gravity effects.

Keywords: Quantum Gravity, Gauge Field Theory, Emergent Geometry, U (1) Gauge Group, Renormalizability, Unitarity, Effective Field Theory