arXiv subjects

Ken-ji Hamada

Publications and source records attributed to Ken-ji Hamada.

At least 19 recordsLinked to original sources

arXiv2026

Ostrogradsky's Theorem is Incompatible with Background Independence in Quantum Gravity

Ostrogradsky's theorem shows that higher-derivative dynamical systems inevitably yields a Hamiltonian featuring a ghost mode that is unbounded from below. However, we argue that this theorem is inapplicable to gravitational systems, as the Hamiltonian constraint, which encodes background independence by dictating that the total Hamiltonian vanishes, holds strictly. The ghost mode obeying this constraint constitutes an indispensable component in the construction of space and time. Nevertheless, it should be underscored that the use of the weak-field (graviton) approximation, being a background-dependent scheme presupposing the existence of absolute time, invokes this theorem; consequently, it is allowed only in the domain below the Planck scale, where second derivative terms dominate.

gr-qc↗

arXiv2024

Quantum Gravity Effective Action Provides Entropy of The Universe

The effective action in renormalizable quantum theory of gravity provides entropy because the total Hamiltonian vanishes. Since it is a renormalization group invariant that is constant in the process of cosmic evolution, we can show conservation of entropy, which is an ansatz in the standard cosmology. Here, we study renormalizable quantum gravity that exhibits conformal dominance at high energy beyond the Planck scale. The current entropy of the universe is derived by calculating the effective action under the scenario of quantum gravity inflation caused by its dynamics. We then argue that ghost modes must be unphysical but are necessary for the Hamiltonian to vanish and for entropy to exist in gravitational systems.

hep-th↗

arXiv2023

Study of Nonlinear Evolution of Spacetime Fluctuations in Quantum Gravity Inflation for Deriving Primordial Spectrum

We study the evolution of quantum fluctuations of gravity around an inflationary solution in renormalizable quantum gravity, in which the initial scalar-fluctuation dominance is shown by the background-free nature expressed by a special conformal invariance. Inflation ignites at the Planck scale and continues until spacetime phase transition occurs at a dynamical scale about $10^{17}$GeV. We can show that during inflation, the initially large scale-invariant fluctuations reduce in amplitude to the appropriate magnitude suggested by tiny CMB anisotropies. The goal of this research is to derive the spectra of scalar fluctuations at the phase transition point, that is, the primordial spectra. A system of nonlinear evolution equations for the fluctuations is derived from the quantum gravity effective action. The running coupling constant is then expressed by a time-dependent average following the spirit of the mean field approximation. In this paper, we determine and examine various nonlinear terms, not treated in previous studies such as the exponential factor of the conformal mode. These contributions occur during the early stage of inflation when the amplitude is still large. Moreover, in order to verify their effects concretely, we numerically solve the evolution equation by making a simplification to extract the most contributing parts of the terms in comoving momentum space. The result indicates that they serve to maintain the initial scale invariance over a wide range beyond the comoving Planck scale. This is a challenge toward the derivation of the precise primordial spectra, and we expect in the future that it will lead to the resolution of the tensions that have arisen in cosmology.

hep-th↗

arXiv2022

Revealing A Trans-Planckian World Solves The Cosmological Constant Problem

The Planck scale is usually believed to be an unpassable wall. Putting a cutoff there and thinking of it as a quantized spacetime entity shows that. However, this is exactly the cause of many problems in quantum gravity. The cosmological constant problem also comes down to the problem of how to describe a trans-Planckian world by a continuum theory that shall be renormalizable and background free. Here, we show that when quantizing gravity in a diffeomorphism-invariant method, in which background freedom arises asymptotically as an exact conformal symmetry, the zero-point energy vanishes identically. Thus, there is no problem with the cosmological constant, which is a physical constant, namely a renormalization group invariant. We also argue that new quanta based on the background freedom emerge and spacetime is discretized dynamically. Primordial fluctuations will originate from such quanta.

hep-th↗

arXiv2020

Diffeomorphism Invariance Demands Conformal Anomalies

We study a series of the Wess-Zumino actions obtained by repeatedly integrating conformal anomalies with respect to the conformal-factor field that appear at higher loops. We show that they arise as physical quantities required to make nonlocal loop correction terms diffeomorphism invariant. Specifically, in a conformally flat spacetime $ds^2=e^{2\phi}(-d\eta^2 + d{\bf x}^2)$, we find that effective actions are described in terms of momentum squared expressed as a physical $Q^2 = q^2/e^{2\phi}$ for $q^2$ measured by the flat metric, which recalls the relationship between physical momentum and comoving momentum in cosmology. It is confirmed by calculating the effective action of QED in such a curved spacetime at the 3-loop level using dimensional regularization. The same applies to the case of QCD, in which we show that the effective action can be summarized in the form of the reciprocal of a running coupling constant squared described by the physical momentum. We also see that the same holds for renormalizable quantum conformal gravity and that conformal anomalies are indispensable for formulating the theory.

hep-th↗

arXiv2020

Localized massive excitation of quantum gravity as a dark particle

We construct a static and spherical excited state without singularities in renormalizable quantum gravity with background-free nature asymptotically. Its diameter is given by a correlation length of the quantum gravity, longer than the Planck length by 2 orders of magnitude, and it has a Schwarzschild tail outside. The quantum gravity dynamics inside is described by employing a nonperturbative expression of higher-order corrections assumed from a physical requirement that the dynamics disappear at the edge where it is in strong coupling. A running coupling constant that is a manifestation of nonlinearity and nonlocality is managed by approximating it as a mean field that depends on the radial coordinate. If the mass is several times the Planck mass, we can set up a system of linearized equations of motion for the gravitational potentials incorporating the running effect and obtain the excited state as its solution. It may be a candidate for dark matter, and will give a new perspective on black hole physics.

hep-th↗

arXiv2017

BRST Conformal Symmetry as A Background-Free Nature of Quantum Gravity

Quantum gravity that describes the world beyond the Planck scale should be formulated in a background-metric independent manner. Such a background-free nature can be represented as a gauge equivalency under conformal transformations, called the BRST conformal symmetry. In this review, we present quantum field theories of gravity with such symmetry. Since we can choose any background owing to this symmetry as far as it is conformally flat, we here employ the cylindrical background. First, we briefly review the famous BRST Liouville-Virasoro algebra in 2D quantum gravity on $R \times S^1$. We then present recent developments of the BRST conformal algebra and physical states of 4D quantum gravity on $R \times S^3$ whose conformal-factor dynamics is ruled by the Riegert's Wess-Zumino action, which arises in the UV limit of the renormalizable quantum conformal gravity with the "asymptotic background freedom". We find that the BRST conformal invariance makes all physical states real and scalar as well as all negative-metric modes unphysical. We also briefly discuss the dynamics of how the conformal invariance breaks down and how our classical spacetime emerges at low energies, in which a novel interpretation of the "minimal length" we can measure comes out without discretizing spacetime.

hep-th↗

arXiv2017

Physical Cosmological Constant in Asymptotically Background Free Quantum Gravity

We study the effective potential in renormalizable quantum gravity with a single dimensionless conformal coupling without a Landau pole. In order to describe a background-free dynamics at the Planck scale and beyond, the conformal-factor field is quantized exactly in a nonperturbative manner. Since this field does not receive renormalization, the field-independent constant in the effective potential becomes itself invariant under the renormalization group flow. That is to say, it gives the physical cosmological constant. We explicitly calculate the physical cosmological constant at the one-loop level in the Landau gauge. We find that it is given by a function of renormalized quantities of the cosmological constant, the Planck mass and the coupling constant, and it should be the observed value. It will give a new perspective on the cosmological constant problem free from an ultraviolet cutoff.

hep-th↗

arXiv2015

Two-Loop Quantum Gravity Corrections to Cosmological Constant in Landau Gauge

The anomalous dimensions of the Planck mass and the cosmological constant are calculated in a renormalizable quantum conformal gravity with a single dimensionless coupling, which is formulated using dimensional regularization on the basis of Hathrell's works for conformal anomalies. The dynamics of the traceless tensor field is handled by the Weyl action, while that of the conformal-factor field is described by the induced Wess-Zumino actions, including the Riegert action as the kinetic term. Loop calculations are carried out in Landau gauge in order to reduce the number of Feynman diagrams as well as to avoid some uncertainty. Especially, we calculate two-loop quantum gravity corrections to the cosmological constant. It suggests that there is a dynamical solution to the cosmological constant problem.

hep-th↗

arXiv2014

RG Analysis for Quantum Gravity with A Single Dimensionless Coupling

We study the quantum conformal gravity whose dynamics is governed by a single dimensionless gravitational coupling with negative beta function. Since the Euler term is not dynamical classically, the constant in front of it is not an independent coupling. Quantum mechanically, however, it induces the Riegert conformal-factor dynamics with BRST conformal symmetry representing background free nature. In this paper, we propose how to handle the Euler term systematically incorporating such dynamics on the basis of renormalization group analysis using dimensional regularization. As a non-trivial test of renormalization, we explicitly calculate the three-loop anomalous dimension of the cosmological constant operator and show that it agrees with the exact expression derived using the BRST conformal symmetry. The physical significance to inflation and CMB is also discussed.

hep-th↗

arXiv2014

Determination of Gravitational Counterterms Near Four Dimensions from RG Equations

The finiteness condition of renormalization gives a restriction on the form of the gravitational action. By reconsidering the Hathrell's RG equations for massless QED in curved space, we determine the gravitational counterterms and the conformal anomalies as well near four dimensions. As conjectured for conformal couplings in 1970s, we show that at all orders of the perturbation they can be combined into two forms only: the square of the Weyl tensor in $D$ dimensions and $E_D=G_4 +(D-4)χ(D)H^2 -4χ(D) \nabla^2 H$, where $G_4$ is the usual Euler density, $H=R/(D-1)$ is the rescaled scalar curvature and $χ(D)$ is a finite function of $D$ only. The number of the dimensionless gravitational couplings is also reduced to two. $χ(D)$ can be determined order by order in series of $D-4$, whose first several coefficients are calculated. It has a universal value of $1/2$ at $D=4$. The familiar ambiguous $\nabla^2 R$ term is fixed. At the $D \to 4$ limit, the conformal anomaly $E_D$ just yields the combination $E_4=G_4-2\nabla^2 R/3$, which induces Riegert's effective action.

hep-th↗

arXiv2012

BRST Analysis of Physical Fields and States for 4D Quantum Gravity on R x S^3

We consider the background-free quantum gravity based on conformal gravity with the Riegert-Wess-Zumino action, which is formulated in terms of a conformal field theory. Employing the $R \times S^3$ background in practice, we construct the nilpotent BRST operator imposing diffeomorphism invariance. Physical fields and states are analyzed, which are given only by real primary scalars with a definite conformal weight. With attention to the presence of background charges, various significant properties, such as the state-operator correspondence and the norm structure, are clarified with some examples.

hep-th↗

arXiv2012

BRST Invariant Higher Derivative Operators in 4D Quantum Gravity based on CFT

We continue the study of physical fields for the background free 4D quantum gravity based on the Riegert-Wess-Zumino action, developed in Phys. Rev. D {\bf 85} (2012) 024028. The background free model is formulated in terms of a certain conformal field theory on M^4 in which conformal symmetry arises as gauge symmetry, namely diffeomorphism invariance. In this paper, we construct the physical field operator corresponding to any integer power of Ricci scalar curvature in the context of the BRST quantization. We also discuss how to define the correlation function and its physical meanings.

hep-th↗

arXiv2011

Background Free Quantum Gravity based on Conformal Gravity and Conformal Field Theory on M^4

We study four dimensional quantum gravity formulated as a certain conformal field theory at the ultraviolet fixed point, whose dynamics is described by the combined system of Riegert-Wess-Zumino and Weyl actions. Background free nature comes out as quantum diffeomorphism symmetry by quantizing the conformal factor of the metric field nonperturbatively. In this paper, Minkowski background M^4 is employed in practice. The generator of quantum diffeomorphism that forms conformal algebra is constructed. Using it, we study the composite scalar operator that becomes a good conformal field. We find that physical fields are described by such scalar fields with conformal dimension 4. Consequently, tensor fields outside the unitarity bound are excluded. Computations of quantum algebra on M^4 are carried out in the coordinate space using operator products of the fields. The nilpotent BRST operator is also constructed.

hep-th↗

arXiv2011

Vertex Operators in 4D Quantum Gravity Formulated as CFT

We study vertex operators in 4D conformal field theory derived from quantized gravity, whose dynamics is governed by the Wess-Zumino action by Riegert and the Weyl action. Conformal symmetry is equal to diffeomorphism symmetry in the ultraviolet limit, which mixes positive-metric and negative-metric modes of the gravitational field and thus these modes cannot be treated separately in physical operators. In this paper, we construct gravitational vertex operators such as the Ricci scalar, defined as space-time volume integrals of them are invariant under conformal transformations. Short distance singularities of these operator products are computed and it is shown that their coefficients have physically correct sign. Furthermore, we show that conformal algebra holds even in the system perturbed by the cosmological constant vertex operator as in the case of the Liouville theory shown by Curtright and Thorn.

hep-th↗

arXiv2010

From CFT Spectra to CMB Multipoles in Quantum Gravity Cosmology

We study the inflation process of universe based on the renormalizable quantum gravity formulated as a conformal field theory (CFT). We show that the power-law CFT spectrum approaches to that of the Harrison-Zel'dovich-Peebles type as the amplitude of gravitational potential gradually reduces during the inflation. The non-Gaussanity parameter is preserved within order of unity due to the diffeomorphism invariance. Sharp fall-off of the angular power spectrum of cosmic microwave background (CMB) at large scale is understood as a consequence of the existence of dynamical scale of the quantum gravity Λ_QG (\simeq 10^{17})GeV. The angular power spectra are computed and compared with the WMAP5 and ACBAR data with a quality of χ^2/dof \simeq 1.1.

astro-ph.CO↗

arXiv2009

Renormalizable 4D Quantum Gravity as A Perturbed Theory from CFT

We study the renormalizable quantum gravity formulated as a perturbed theory from conformal field theory (CFT) on the basis of conformal gravity in four dimensions. The conformal mode in the metric field is managed non-perturbatively without introducing its own coupling constant so that conformal symmetry becomes exact quantum mechanically as a part of diffeomorphism invariance. The traceless tensor mode is handled in the perturbation with a dimensionless coupling constant indicating asymptotic freedom, which measures a degree of deviation from CFT. There are no massive ghosts because they are not gauge invariant in this formulation. Higher order renormalization is carried out using dimensional regularization, in which the Wess-Zumino integrability condition is applied to reduce indefiniteness existing in higher-derivative actions. The effective action of quantum gravity improved by renormalization group is obtained. We then make clear that conformal anomalies are indispensable quantities to preserve diffeomorphism invariance. Anomalous scaling dimensions of the cosmological constant and the Planck mass are calculated. The effective cosmological constant is obtained in the large number limit of matter fields.

hep-th↗

arXiv2009

Conformal Field Theory on R x S^3 from Quantized Gravity

Conformal algebra on R x S^3 derived from quantized gravitational fields is examined. The model we study is a renormalizable quantum theory of gravity in four dimensions described by a combined system of the Weyl action for the traceless tensor mode and the induced Wess-Zumino action managing non-perturbative dynamics of the conformal factor in the metric field. It is shown that the residual diffeomorphism invariance in the radiation^+ gauge is equal to the conformal symmetry, and the conformal transformation preserving the gauge-fixing condition that forms a closed algebra quantum mechanically is given by a combination of naive conformal transformation and a certain field-dependent gauge transformation. The unitarity issue of gravity is discussed in the context of conformal field theory. We construct physical states by solving the conformal invariance condition and calculate their scaling dimensions. It is shown that the conformal symmetry mixes the positive-metric and the negative-metric modes and thus the negative-metric mode does not appear independently as a gauge invariant state at all.

hep-th↗