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It is well known that General Relativity cannot be considered under the standard of a perturbatively renormalizable quantum field theory, but asymptotic safety is taken into account as a possibility for the formulation of gravity as a…

Usually, General Relativity (GR) is known to be unrenormalizable perturbatively from the viewpoint of quantum field theory. But in the modern sense of renormalizability, there still remains the possibility to investigate whether GR is…

The basic features of a quantum field theory which is Poincar\'e invariant, gauge invariant, finite and unitary to all orders of perturbation theory are reviewed. Quantum gravity is finite and unitary to all orders of perturbation theory.…

We extend the general framework of perturbative quantum field theory developped for the pure Yang-Mills model to gravity. First we present a variant of the elimination procedure of the anomalies in the second order of perturbation theory.…

We find considerable evidence supporting the conjecture that four-dimensional Quantum Einstein Gravity is ``asymptotically safe'' in Weinberg's sense. This would mean that the theory is likely to be nonperturbatively renormalizable and thus…

Hawking radiation and Bekenstein--Hawking entropy are the two robust predictions of a yet unknown quantum theory of gravity. Any theory which fails to reproduce these predictions is certainly incorrect. While several approaches lead to…

One of the obstacles to reconciling quantum theory with general relativity, is constructing a theory which is both consistent with observation, and and gives finite answers at high energy, so that the theory holds at arbitrarily short…

It is well known that Einstein gravity is non-renormalizable; however a generalized approach is proposed that leads to Einstein gravity {\it after} renormalization. This them implies that at least one candidate for quantum gravity treats…

We search for a universal property of quantum gravity. By "universal", we mean the independence from any existing model of quantum gravity (such as the super string theory, loop quantum gravity, causal dynamical triangulation, and so on).…

We propose a covariant entropy bound in gravitational theories beyond general relativity (GR), using Wald-Jacobson-Myers entropy instead of Bekenstein-Hawking entropy. We first extend the proof of the bound known in 4-dimensional GR to…

We study the effect of self-gravity on entropy by directly solving the 4D semi-classical Einstein equation. In particular, we focus on whether the Bekenstein-Hawking formula holds when self-gravity is extremely strong. As an example, we…

The quantum gravity is formulated based on gauge principle. The model discussed in this paper has local gravitational gauge symmetry and gravitational field is represented by gauge potential. A preliminary study on gravitational gauge group…

Renormalization procedure is generalized to be applicable for non renormalizable theories. It is shown that introduction of an extra expansion parameter allows to get rid of divergences and express physical quantities as series of finite…

This paper consists of three steps. In the first, we prove that the Bekenstein-Hawking entropy is the unique expression of black hole entropy. Our proof is constructed in the framework of thermodynamics without any statistical discussion.…

We review recent progress with the understanding of quantum fields, including ideas how gravity might turn out to be a renormalizable theory after all.

The quantum gravity is formulated based on principle of local gauge invariance. The model discussed in this paper has local gravitational gauge symmetry and gravitational field appears as gauge field. The problems on quantization and…

The asymptotic safety scenario of Quantum Einstein Gravity, the quantum field theory of the spacetime metric, is reviewed and it is argued that the theory is likely to be nonperturbatively renormalizable. It is also shown that asymptotic…

This work explores an alternative solution to the problem of renormalizability in Einstein gravity. In the proposed approach, Einstein gravity is transformed into the renormalizable theory of four-derivative gravity by applying a field…

The quantum gauge general relativity is proposed in the framework of quantum gauge theory of gravity. It is formulated based on gauge principle which states that the correct symmetry for gravitational interactions should be gravitational…

We evaluate the quantum corrections of the Einstein-Hilbert action with boundaries in the $2+\epsilon$ dimensional expansion approach. We find the Einstein-Hilbert action with boundaries to be renormalizable to the one loop order. We…