A Coherent Approach towards Quantum Gravity

Abstract

This paper typically focuses on the rescaling or equivocally a phase transition from the asymptotic approach of renormalizing the quantum gravity 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 as the basis of the unified theory. To construct a successful Ultraviolet (UV) completed theory via the fixed-point renormalization group flow equations (FRGE) results in an asymptotic safety approach of the quantum gravity (QG). From the loop-(2) onwards, the higher derivative divergence terms like the higher derivative curvatures, and quadratic divergences with higher derivative scalars make the momentum go to infinity which assaults a problem in renormalizing the QG. If the Einstein-Hilbert (E-H) action, which is the principle of least action is being computed, arising an equation of motion, 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, and based on that localization principle, the entire path integral got collapsed to isolated points or granules that if corresponds the aforesaid actions, results in negating the divergences’ with an implied bijections’ and reverse bijections’ of a diffeomorphism of a continuous differentiable functional domains. If those domains are being attributed to the spatial constraints, Hamiltonian constraints, and Master constraints then, through Ashtekar variables, it can be modestly shown that the behavior of quantum origin of asymptotic safety behavior is similar to the LQG granules of spin foam spacetime. Then, we will proceed with the triangulation of the “zoomed in” 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.