Phase structure of dynamical triangulation models in three dimensions

The dynamical triangulation model of three-dimensional quantum gravity is shown to have a line of transitions in an expanded phase diagram which includes a coupling μ to the order of the vertices. Monte Carlo renormalization group and finite size scaling techniques are used to locate and characterize this line. Our results indicate that for μ < μ₁ ∼ −1.0 the model is always in a crumpled phase independent of the value of the curvature coupling. For μ < 0 the results are in agreement with an approximate mean field treatment. We find evidence that this line corresponds to first-order transitions extending to positive μ. However, the behavior appears to change for μ > μ₂ ∼ 2.0−4.0. The simplest scenario that is consistent with the data is the existence of a critical end point.     

Quantum quenches and off-equilibrium dynamical transition in the infinite-dimensional Bose-Hubbard model

We study the off-equilibrium dynamics of the infinite-dimensional Bose-Hubbard model after a quantum quench. The dynamics can be analyzed exactly by mapping it to an effective Newtonian evolution. For integer filling, we find a dynamical transition separating regimes of small and large quantum quenches starting from the superfluid state. This transition is very similar to the one found for the fermionic Hubbard model by mean field approximations.     

量子引力中曲率的激发

求出了Stelle可重整引力的量子Wilson圈的h阶首项,得到了矢量平移被定域曲率的激发量子化的结果,求得了非平坦背景下量子Mlson圈的泛函计算式.     

The Spectrum of Quantum Gravity

Physics of Particles and Nuclei Letters - In this paper we consider the degrees of freedom beyond the graviton present in the effective field theory for quantum gravity. We point out that the...     

Causal dynamical triangulation with extended interactions in 1+1 dimensions

We study the Causal Dynamical Triangulation (CDT) with extended interactions in 1+1 dimensions applying the method in the non-critical String Field Theory (SFT) constructed by Ishibashi and Kawai. For this model, we solve Schwinger-Dyson?s Equation (SDE) for disk amplitude perturbatively, and find a matrix model in the continuum limit reproducing the SDE in the non-critical SFT approach as the loop equation.     

Gravitational Collapse in Loop Quantum Gravity

In this paper we study the gravitational collapse applying methods of loop quantum gravity to a minisuperspace model. We consider the space-time region inside the Schwarzschild black hole event horizon and we divide this region in two parts, the first one where the matter (dust matter) is localized and the other (outside) where the metric is Kantowski–Sachs type. We study the Hamiltonian constraint obtaining a set of three difference equations that give a regular and natural evolution beyond the classical singularity point in “r=0” localized.     

Gravitational Collapse in Quantum Einstein Gravity

The existence of spacetime singularities is one of the biggest problems of nowadays physics. According to Penrose, each physical singularity should be covered by a “cosmic censor” which prevents any external observer from perceiving their existence. However, classical models describing the gravitational collapse usually results in strong curvature singularities, which can also remain “naked” for a finite amount of advanced time. This proceedings studies the modifications induced by asymptotically safe gravity on the gravitational collapse of generic Vaidya spacetimes. It will be shown that, for any possible choice of the mass function, quantum gravity makes the internal singularity gravitationally weak, thus allowing a continuous extension of the spacetime beyond the singularity.     

Weave States in Loop Quantum Gravity

Weaves are eigenstates of geometrical operators in nonperturbative quantum gravity, which approximate flat space (or other smooth geometries) at large scales. We describe two such states, which diagonalize the area as well as the volume operators. The existence of such states shows that some earlier worries about the difficulty of realizing kinematical states with non-vanishing volume can be overcome. We also show that the Q operator used in earlier work for extracting geometrical information from quantum states does not capture more information than the area and volume operators.     

Symmetry and Evolution in Quantum Gravity

We propose an operator constraint equation for the wavefunction of the Universe that admits genuine evolution. While the corresponding classical theory is equivalent to the canonical decomposition of General Relativity, the quantum theory contains an evolution equation distinct from standard Wheeler–DeWitt cosmology. Furthermore, the local symmetry principle—and corresponding observables—of the theory have a direct interpretation in terms of a conventional gauge theory, where the gauge symmetry group is that of spatial conformal diffeomorphisms (that preserve the spatial volume of the Universe). The global evolution is in terms of an arbitrary parameter that serves only as an unobservable label for successive states of the Universe. Our proposal follows unambiguously from a suggestion of York whereby the independently specifiable initial data in the action principle of General Relativity is given by a conformal geometry and the spatial average of the York time on the spacelike hypersurfaces that bound the variation. Remarkably, such a variational principle uniquely selects the form of the constraints of the theory so that we can establish a precise notion of both symmetry and evolution in quantum gravity.     

The Quantum Regularization of Singular Black-Hole Solutions in Covariant Quantum Gravity

An excruciating issue that arises in mathematical, theoretical and astro-physics concerns the possibility of regularizing classical singular black hole solutions of general relativity by means of quantum theory. The problem is posed here in the context of a manifestly covariant approach to quantum gravity. Provided a non-vanishing quantum cosmological constant is present, here it is proved how a regular background space-time metric tensor can be obtained starting from a singular one. This is obtained by constructing suitable scale-transformed and conformal solutions for the metric tensor in which the conformal scale form factor is determined uniquely by the quantum Hamilton equations underlying the quantum gravitational field dynamics.     

An Overview of Canonical Quantum Gravity

This paper presents a brief review of currentresults on the canonical quantization of generalrelativity using Ashtekar's variables and loopquantization.     

Renormalizable Quantum Gauge Theory of Gravity

The quantum gravity is formulated based on the principle of local gauge invariance. The model discussed in this paper has local gravitational gauge symmetry, and gravitational field is represented by gauge field. In the leading-order approximation, it gives out classical Newton's theory of gravity. In the first-order approximation and for vacuum, it gives out Einstein's general theory of relativity. This quantum gauge theory of gravity is a renormalizable quantum theory.     

Midisuperspace Models of Canonical Quantum Gravity

A midisuperspace model is a field theoryobtained by symmetry reduction of a parent gravitationaltheory. Such models have proven useful for exploring theclassical and quantum dynamics of the gravitational field. I present three recent classes ofresults pertinent to canonical quantization of vacuumgeneral relativity in the context of midisuperspacemodels. (1) I give necessary and sufficient conditions such that a given symmetry reduction can beperformed at the level of the Lagrangian or Hamiltonian.(2) I discuss the Hamiltonian formulation of modelsbased upon cylindrical and toroidal symmetry. In particular, I explain how these models can beidentified with parametrized field theories of wavemaps; thus a natural strategy for canonical quantizationis available. (3) The quantization of a parametrized field theory, such as the midisuperspace modelsconsidered in (2), requires construction of a quantumfield theory on a fixed (flat) spacetime that allows fortime evolution along arbitrary foliations of spacetime. I discuss some recent results on thepossibility of finding such a quantum fieldtheory.     

Renormalizable Quantum Gauge Theory of Gravity

The quantum gravity is formulated based on the principle of local gauge invariance. The model discussedin this paper has local gravitational gauge symmetry, and gravitational field is represented by gauge field. In the leading-order approximation, it gives out classical Newton‘s theory of gravity. In the first-order approximation and for vacuum,it gives out Einstein‘s general theory of relativity. This quantum gauge theory of gravity is a renormalizable quantumtheory.     

The length operator in Loop Quantum Gravity

The dual picture of quantum geometry provided by a spin network state is discussed. From this perspective, we introduce a new operator in Loop Quantum Gravity—the length operator. We describe its quantum geometrical meaning and derive some of its properties. In particular we show that the operator has a discrete spectrum and is diagonalized by appropriate superpositions of spin network states. A series of eigenstates and eigenvalues is presented and an explicit check of its semiclassical properties is discussed.