A Coherent Approach Towards Quantum Gravity
This paper focuses on a phase transition from the asymptotic safety approach of renormalizing the quantum gravity (QG) to a more granular approach of the loop quantum gravity (LQG) and then merging it with the Regge calculus for deriving the spin-(2) graviton. From loop-(2) onwards, the higher derivative curvatures make the momentum go to infinity which assaults a problem in renormalizing the QG. If the Einstein-Hilbert (E-H) action, is computed, and a localized path integral (or partition functions) is defined over a curved space, then that action is shown to be associated with the higher order dimension in a more compactified way, resulting in an infinite winding numbers being accompanied through the exponentiality coefficients of the partition integrals in the loop expansions of the second order term onwards. Based on that localization principle, the entire path integral got collapsed to discrete points that if corresponds the aforesaid actions, results in negating the divergences’ with an implied bijections’ and reverse bijections’ of a diffeormorphism of a continuous differentiable functional domains. If those domains are being attributed to the spatial constraints, Hamiltonian constraints and Master constraints then, through Ashtekar’s variables, it can be modestly shown that the behavior of quantum origin of asymptotic safety is similar to the LQG granules of spinfoam spacetime. Then, we will proceed with the triangulation of the entangled-points that results in the inclusion of Regge poles via the quantum number (+2,-2,0) as the produced variables of the spin-(2) graviton and spin-(0) dilaton.