Deriving Einstein’s Field Equations from Loop Quantum Gravity Theory

is paper explores how to derive Einstein’s field equations from Loop Quan?tum Gravity (LQG) theory. Loop Quantum Gravity is a theory that attempts tounify general relativity with quantum mechanics, with the core idea of discretizingspacetime and using spin networks to describe quantum states. This paper com?bines mathematical tools such as fractal geometry and non-commutative geometryto detail the process of transitioning from the discrete spacetime structure of loopquantum gravity to the continuous spacetime structure of classical general relativ?ity, ultimately deriving Einstein’s field equations. By introducing concepts such asfractal curvature and fractal path integrals, this paper provides new mathemati?cal tools and perspectives for loop quantum gravity theory, further advancing thedevelopment of quantum gravity theory.