Quantum Principle of Relativity and The Renormalizable Quantum Gravity

Abstract: We develop a purely quantum theory based on the novel principle of relativity, termed the quantum principle of relativity, instead of applying the diffeomorphism invariance. We demonstrate that the essence of the principle of relativity can be naturally extended into the quantum realm, maintaining the identical structures of active and passive transformations. By employing this principle, we show that quantum gravitational effects are naturally incorporated into the renormalizable theory, with general relativity emerging in large distances. We derive graviton propagators and provide several examples grounded in this novel theory.