Quantum Gravitational Field

Abstract

We propose an asymptotically safe framework for quantum gravity, centered on the gravitational spinor (GS, ψ ^ A B C D ) as the fundamental quantum field describing vacuum gravitational fluctuations. As a massless spin-2 field, the GS satisfies the equation of motion ∂ A A ′ ψ ^ A B C D = 0 , and is further extended to the nonlinear regime via □ ψ ^ A B C D − 4 λ ψ ^ A B C D ( ψ ^ E F G H ψ ^ E F G H ) = J A B C D in the presence of sources, providing a unified description encompassing both perturbative gravitons and non-perturbative gravitational solitons. This formulation maintains consistency with the quantized Einstein equations while encodes spacetime curvature via the relation C ^ μ ν ρ σ = κ ψ ^ A B C D ( σ μ ρ A B σ ν σ C D − σ μ σ A B σ ν ρ C D ) . Functional renormalization group (FRG) analysis reveals that the GS framework possesses a non-trivial ultraviolet fixed point, demonstrating asymptotic safety. It thereby joins the ranks of other well-established quantum gravity approaches—such as loop quantum gravity (LQG) and string theory—as one of the few promising candidates for a renormalizable quantum theory of gravity. This marks significant progress in addressing UV divergences and background independence. Through generalized gauge equation (GGE) transformations, the GS can be induced from other quantized gauge fields (e.g., electromagnetic, weak, and strong fields), suggesting a unification of the four fundamental interactions. Gravitational interactions are mediated by virtual GS exchange, with the Newtonian limit recovered at low energies. High-energy predictions include GS coherent states under extreme electromagnetic fields (~10 20 W/m 2 ) and detectable gravitational wave soliton signals (verifiable via LIGO), opening new avenues for experimental tests of quantum gravity. This framework not only offers a geometric perspective on unification but also advances quantum gravity research through asymptotic safety and observable phenomena.