A Coherent Approach towards Quantum Gravity

Deep Bhattacharjee *

Theoretical Physics Research Division of AATWRI Aerospace and Defense Research Directorate, India and Electro Gravitational Space Propulsion Laboratory, India.

*Author to whom correspondence should be addressed.


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.

Keywords: Localization, partition functions, asymptotic safety, loop quantum gravity, Einstein-Hilbert action, renormalized fixed flow, master constraints, Regge poles, Yukawa potential

How to Cite

Bhattacharjee, D. (2022). A Coherent Approach towards Quantum Gravity. Physical Science International Journal, 26(6), 59–78. https://doi.org/10.9734/psij/2022/v26i6751


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Piguet O. Loop Quantum Gravity. Astronomische Nachrichten. 2014;335(6–7):721–726.


Rovelli C. Loop quantum gravity. Encyclopedia of Mathematical Physics. 2006:339-343.


Wetterich C. Effective scalar potential in asymptotically safe quantum gravity. Universe. 2021;7(2):45.


Litim D, Sannino F. Asymptotic safety guaranteed. JHEP. 2014;1412:178

Available:https://doi.org/10.1007/JHEP12(2014)178 [arXiv:1406.2337 [hep-th].

Weinberg S. Ultraviolet divergences in quantum theories of gravitation; 1979

Niedermaier M, Reuter M. “The asymptotic safety scenario in quantum gravity.” Living Rev. Rel. 2006:9:5.


Reuter M. “Nonperturbative evolution equation for quantum gravity.” Phys. Rev. D. 1998;57:971.

Available:https://doi.org/10.1103/PhysRevD.57.971 [hep-th/9605030].

Reuter M. Saueressig F. “Quantum gravity and the functional renormalization group: The road towards asymptotic safety.” Cambridge University Press, Cambridge; 2018.

Lippoldt S. Renormalized functional renormalization group. Physics Letters B. 2018;782:275–279.


Bonini M, Marchesini G. Gauge invariant action at the ultraviolet cutoff. Physics Letters B. 1996;389(3):566–570.


Modesto L, Moffat JW, Nicolini P. Black holes in an ultraviolet complete quantum gravity. Physics Letters B. 2011;695(1-4):397-400.


Lauscher O, Reuter M. Ultraviolet fixed point and generalized flow equation of quantum gravity. Physical Review D. 2001;65(2).


Hooft GT, Veltman MJ. One-loop divergences in the theory of gravitation. Annales De L'Institut Henri Poincaré, A. 1974;1(20):69-94.

Goroff MH, Sagnotti A. The ultraviolet behavior of Einstein gravity. Nuclear Physics B. 1986;266(3-4):709-736.


Eichhorn A. Asymptotically safe gravity; 2020. arXiv:2003.00044v1.

Benini F. Localization in Supersymmetric field theories. YITP Kyoto; 2016.

Quantum electrodynamics. Nature, 1947;160(4056):135–136.


Foda OE. A simple perturbative renormalization scheme for supersymmetric gauge theories. Physics Letters B. 1983;126(3–4):207–214.


Bernardeau F. Gravity- and non-gravity-mediated couplings in multiple-field inflation. Classical and Quantum Gravity. 2010;27(12):124004.


Chudecki A. Congruences of null strings and their relations with weyl tensor and traceless ricci tensor. Acta Physica Polonica B Proceedings Supplement. 2017;10(2):373.


Goroff MH, Sagnotti A. The ultraviolet behavior of Einstein gravity. Nuclear Physics B. 1986;266(3-4):709-736.


Eichhorn A. Asymptotically safe gravity; 2020. arXiv:2003.00044v1.

Banerjee N, Banerjee S, Kumar Gupta R, Mandal I, Sen A. Supersymmetry, localization and quantum entropy function. Journal of High Energy Physics. 2010; (2).


Moffat JW. Ultraviolet complete quantum gravity. Eur. Phys. J. Plus. 2011;126:43.


Wilson KG, Kogut JB. "The renormalization group and the ε expansion". Physics Reports. 1974;12(2):75–199.


Wetterich C. "Exact evolution equation for the effective potential". Phys. Lett. B. 1993;301(1):90–94.


Morris TR. "The exact renormalization group and approximate solutions". International Journal of Modern Physics A. 1994;09(14):2411–2449.


Cho HT, Kantowski R. Unique one-loop effective action for the six-dimensional Einstein-Hilbert action. Physical Review Letters. 1991;67(4):422–425.


Novales-Sánchez H, Toscano JJ. About gauge invariance in compactified extra dimensions. Physical Review D. 2011;84(5).


Schwarz A, Zaboronsky O. Supersymmetry and localization. Communications in Mathematical Physics. 1997;183(2):463–476.


Tronko N, Brizard AJ. Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories. Physics of Plasmas. 2015;22(11):112507.


Ashtekar A. Ashtekar variables. Scholarpedia, 2015;10(6):32900.


Lugiato L. A generalized master equation for time-dependent Hamiltonians. Physica. 1969;44(3):337–344.


Livine E. Intertwiner Entanglement on Spin Networks; 2017.

Available:https://doi.org/10.1103/PhysRevD.97.026009. arXiv:1709.08511v1[gr-qc]

Cooperman JH. Making the case for causal dynamical triangulations. Foundations of Physics, 2015;50(11): 1739–1755.


Bhattacharjee D. M-theory and F-theory over theoretical analysis on cosmic strings and calabi-yau manifolds subject to conifold singularity with randall-sundrum model. Asian Journal of Research and Reviews in Physics. 2022:25–40.


Fort H, Gambini R, Pullin J. Lattice knot theory and quantum gravity in the loop representation. Physical Review D. 1997;56(4):2127–2143.


Pullin J. Knot theory and quantum gravity in loop space. A Primer; 2000. arXiv:hep-th/9301028v2

Williams RM. Discrete quantum gravity: The regge calculus approach. International Journal of Modern Physics B. 1992;06(11n12):2097–2108.


Bethe HA, Kinoshita T. Behavior of regge poles in a potential at large energy. Physical Review. 1962;128(3):1418–1424.