Quantum effects of black holes and the cosmological constant problem

A quantum equation of gravity is proposed using geometric quantization of general relativity. Quantum equation for a black hole is solved using the Wentzel-Kramers-Brillouin (WKB) method. Quantum effects of a Schwarzschild black hole are provided by solving a quantum equation of gravity requiring a stationary phase and also using the Einstein-Brillouin-Keller (EBK) quantization condition, and they are consistent each other. WKB method is also applied to the McVittie-Thakurta metric, which is describing a system consists of Schwarzschild black holes and a scalar field. A possible interplay between quantum black holes and scalar field are investigated in detail. A number density of black holes in the universe is obtained using statistical mechanics on a system consisting of black holes and a scalar filed. A possible solution for the cosmological constant problem is proposed in basis of a statistical consideration.Comment: 13 pages, 1 figur

Consistent simulation of non-resonant diphoton production at hadron collisions with a custom-made parton shower

We have developed a Monte Carlo event generator for non-resonant diphoton ($\gamma\gamma$) production at hadron collisions in the framework of GR@PPA, which consistently includes additional one-jet production. The jet-matching method developed for initial-state jet production has been extended to the final state in order to regularize the final-state QED divergence in the $qg \rightarrow \gamma\gamma + q$ process. A QCD/QED-mixed parton shower (PS) has been developed to complete the matching. The PS has the capability of enforcing hard-photon radiation, and small-$Q^{2}$ photon radiations that are not covered by the PS are supplemented by using a fragmentation function. The generated events can be passed to general-purpose event generators in order to perform the simulations down to the hadron level. Thus, we can simulate the isolation requirements that must be applied in experiments at the hadron level. The simulation results are in reasonable agreement with the predictions from RESBOS and DIPHOX. The simulated hadron-level events can be further fed to detector simulations in order to investigate the detailed performance of experiments.Comment: 23 pages, 15 figure

Quantum GravitoElectromagnetic Dynamics

We propose a renormalisable quantum theory of gravity (QGED) based on the standard BRST quantisation used to quantise the Yang--Mills theory. The BRST-invariant Lagrangian of the gravitationally interacting $U(1)$-gauge theory, including gauge fixing and ghost parts, is provided. From this Lagrangian, we extract a set of Feynman rules in the local inertial frame where gravity vanishes locally. Utilising Feynman rules of the QGED prepared here, we construct all renormalisation constants and show that the theory is perturbatively renormalisable in one-loop order. We replace infinite-valued bare objects in the bare Lagrangian with experimentally measured ones. In addition to standard QED parameters, we show that the gravitational coupling constant is measurable experimentally. We also discuss a running effect of the gravitational coupling constant and the perturbative estimation of the Hawking radiation as examples of the perturbative QGED.Comment: 50 pages, 12 figure

Green's function in general relativity

This report provides Green's functions (classical propagators) of gravitational fields of vierbein and spin-connection in general relativity. The existence of Green's function of the Laplace operator in curved space with an indefinite metric is ensured owing to the Hodge harmonic analysis. The analyticity of Green's function is naturally determined intrinsically, keeping a causality. This report proposed a novel definition of the momentum space in curved space-time and the linearisation of the Einstein equation as a free field consistent with that for the Yang-Mills gauge field. The proposed linearisation does not utilize the weak-field approximation; thus, the method applies to highly caved space-time. We gave two examples of Green's function of gravitational fields, the plane wave solution and the Schwarzschild solution.Comment: 20 pages, 2 figure