Towards a Complete UV-Finite Quantum Gravity: Perturbative and Non-Perturbative Synthesis

Abstract We present a comprehensive formulation of quantum gravity that reconciles perturbative and non-perturbative techniques to achieve a UV-finite, unitary, and generally covariant theory. By carefully incorporating ghost contributions, higher-derivative corrections, and nonlocal exponential form factors, we explicitly demonstrate the cancellation of divergences up to three-loop order in graviton interactions. Canonical quantisation and path integral approaches are synthesised to address non-perturbative effects such as spacetime foam and instanton contributions. Numerical evaluations of loop integrals confirm the suppression of high-energy divergences, while physical implications for graviton scattering, cosmology, and black hole structure are discussed. This framework provides a concrete methodology for bridging classical general relativity with quantum principles while maintaining predictive control at all energy scales.