相关论文: Quantum $R^2$ Gravity in Two Dimensions

The application of quantum theory to gravity is beset with many technical and conceptual problems. After a short tour d'horizon of recent attempts to master those problems by the introduction of new approaches, we show that the aim, a…

In general relativity, there is a well-developed formalism for working with the approximation that a gravitational source is concentrated on a shell, or codimension one surface. By contrast, there are obstacles to concentrating sources on…

We show how the stochastic stabilization provides both the weak coupling genus expansion and a strong coupling expansion of 2d quantum gravity. The double scaling limit is described by a hamiltonian which is unbounded from below, but which…

In quantum systems with many degrees of freedom the replica method is a useful tool to study the entanglement of arbitrary spatial regions. We apply it in a way which allows them to back-react. As a consequence, they become dynamical…

The $2N$-dimensional quantum problem of $N$ particles (e.g. electrons) with interaction $\beta/r^2$ in a two-dimensional parabolic potential $\omega_0$ (e.g. quantum dot) and magnetic field $B$, reduces exactly to solving a…

The macroscopic dimensions of space should not be input but rather output of a general model for physics. Here, dimensionality arises from a recently discovered mathematical bifurcation: positive versus indefinite manifold pairings. It is…

Spontaneous compactification ---on a $R^1\times S^1$ background--- in 2D induced quantum gravity (considered as a toy model for more fundamental quantum gravity) is analyzed in the gauge-independent effective action formalism. It is shown…

We describe a theory of quantum gravity which is based on the assumption that the spacetime structure at small distances is given by a piecewise linear (PL) 4-manifold corresponding to a triangulation of a smooth 4-manifold. The fundamental…

We show how it is possible to formulate Euclidean two-dimensional quantum gravity as the scaling limit of an ordinary statistical system by means of dynamical triangulations, which can be viewed as a discretization in the space of…

General relativity promotes space-time to a physical, dynamical object subject to equations of motion. Quantum gravity, accordingly, must provide a quantum framework for space-time, applicable on the smallest distance scales. Just like…

We discuss a basis for the nonperturbative Hilbert space of quantum gravity with one asymptotic boundary. We use this basis to show that the Hilbert space for gravity with two disconnected boundaries factorizes into a product of two copies…

An important task faced by all approaches of quantum gravity is to incorporate superpositions and quantify quantum uncertainties of spacetime causal relations. We address this task in 2D. By identifying a global $Z_2$ symmetry of 1+1D…

We study 2D quantum gravity on spherical topologies using the Regge calculus approach. Our goal is to shed new light upon the validity of the Regge approach to quantum gravity, which has recently been questioned in the literature. We…

One can try to define the theory of quantum gravity as the sum over geometries. In two dimensions the sum over {\it Euclidean} geometries can be performed constructively by the method of {\it dynamical triangulations}. One can define a {\it…

It has been recently claimed [arXiv:1102.3434] that quantum gravity models where the number of dimensions reduces at the ultraviolet exhibit a potentially observable cutoff in the primordial gravitational wave spectrum, and that this is a…

In this paper we have calculated the spectral dimension of loop quantum gravity (LQG) using simple arguments coming from the area spectrum at different length scales. We have obtained that the spectral dimension of the spatial section runs…

This thesis discusses the topological aspects of quantum gravity, focusing on the connection between 2D quantum gravity and 2D topological gravity. The mathematical background for the discussion is presented in the first two chapters. The…

The central principle of affine quantum gravity is securing and maintaining the strict positivity of the matrix $\{\hg_{ab}(x)\}$ composed of the spatial components of the local metric operator. On spectral grounds, canonical commutation…

The microscopic theories of quantum gravity related to integrable lattice models can be constructed as special deformations of pure gravity. Each such deformation is defined by a second order differential operator acting on the coupling…

For the purpose of analyzing observed phenomena, it has been convenient, and thus far sufficient, to regard gravity as subject to the deterministic principles of classical physics, with the gravitational field obeying Newton's law or…