7,380 research outputs found
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.Comment: 43 pages, eqs.(3.9) and (6.18) correcte
Quantum Gravity and Black Hole Dynamics in 1+1 Dimensions
We study the quantum theory of 1+1 dimensional dilaton gravity, which is an
interesting toy model of the black hole dynamics. The functional measures are
explicitly evaluated and the physical state conditions corresponding to the
Hamiltonian and the momentum constraints are derived. It is pointed out that
the constraints form the Virasoro algebra without central charge. In ADM
formalism the measures are very ambiguous, but in our formalism they are
explicitly defined. Then the new features which are not seen in ADM formalism
come out. A singularity appears at \df^2 =\kappa (>0) , where and is the number of matter fields. Behind the singularity
the quantum mechanical region \kappa > \df^2 >0 extends, where the sign of
the kinetic term in the Hamiltonian constraint changes. If , the
singularity disappears. We discuss the quantum dynamics of black hole and then
give a suggestion for the resolution of the information loss paradox. We also
argue the quantization of the spherically symmetric gravitational system in 3+1
dimensions. In appendix the differences between the other quantum dilaton
gravities and ours are clarified and our status is stressed.Comment: phyztex, UT-Komaba 92-14. A few misleading sentences are corrected
and some references are adde
Simple Problems: The Simplicial Gluing Structure of Pareto Sets and Pareto Fronts
Quite a few studies on real-world applications of multi-objective
optimization reported that their Pareto sets and Pareto fronts form a
topological simplex. Such a class of problems was recently named the simple
problems, and their Pareto set and Pareto front were observed to have a gluing
structure similar to the faces of a simplex. This paper gives a theoretical
justification for that observation by proving the gluing structure of the
Pareto sets/fronts of subproblems of a simple problem. The simplicity of
standard benchmark problems is studied.Comment: 10 pages, accepted at GECCO'17 as a poster paper (2 pages
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.Comment: 26 pages, rewrote review part concisely, added explanation
CMB Anisotropies Reveal Quantized Gravity
A novel primordial spectrum with a dynamical scale of quantum gravity origin
is proposed to explain the sharp fall off of the angular power spectra at low
multipoles in the COBE and WMAP observations. The spectrum is derived from
quantum fluctuations of the scalar curvature in a renormalizable model of
induced gravity. This model describes the very early universe by the conformal
field fluctuating about an inflationary background with the expansion time
constant of order of the Planck mass.Comment: 12 pages, 2 figure
Recursion Relations in Liouville Gravity coupled to Ising Model satisfying Fusion Rules
The recursion relations of 2D quantum gravity coupled to the Ising model
discussed by the author previously are reexamined. We study the case in which
the matter sector satisfies the fusion rules and only the primary operators
inside the Kac table contribute. The theory involves unregularized divergences
in some of correlators. We obtain the recursion relations which form a closed
set among well-defined correlators on sphere, but they do not have a beautiful
structure that the bosonized theory has and also give an inconsistent result
when they include an ill-defined correlator with the divergence. We solve them
and compute the several normalization independent ratios of the well-defined
correlators, which agree with the matrix model results.Comment: Latex, 22 page
Making a Universe
For understanding the origin of anisotropies in the cosmic microwave
background, rules to construct a quantized universe is proposed based on the
dynamical triangulation method of the simplicial quantum gravity. A
-dimensional universe having the topology is created numerically in
terms of a simplicial manifold with -simplices as the building blocks. The
space coordinates of a universe are identified on the boundary surface , and the time coordinate is defined along the direction perpendicular
to . Numerical simulations are made mainly for 2-dimensional
universes, and analyzed to examine appropriateness of the construction rules by
comparing to analytic results of the matrix model and the Liouville theory.
Furthermore, a simulation in 4-dimension is made, and the result suggests an
ability to analyze the observations on anisotropies by comparing to the scalar
curvature correlation of a -surface formed as the last scattering
surface in the universe.Comment: 27pages,18figures,using jpsj.st
- …