Related papers: The Weak-Coupling Limit of Simplicial Quantum Grav…
The strong coupling physics of two dimensional gravity at $C=7$, $13$, $19$ is summarized. It is based on a new set of local fields which do not preserve chirality. Thus this quantum number becomes ``deconfined'' in the strongly coupled…
A crucial problem in quantum cosmology is a careful analysis of the one-loop semiclassical approximation for the wave function of the universe, after an appropriate choice of mixed boundary conditions. The results for Euclidean quantum…
A model of simplicial quantum gravity in three dimensions is investigated numerically based on the technique of the dynamical triangulation (DT). We are concerned with the surfaces appearing on boundaries (i.e., sections) of…
Four-dimensional(4D) spacetime structures are investigated using the concept of the geodesic distance in the simplicial quantum gravity. On the analogy of the loop length distribution in 2D case, the scaling relations of the boundary volume…
We extend here the canonical treatment of spherically symmetric (quantum) gravity to the most simple matter coupling, namely spherically symmetric Maxwell theory with or without a cosmological constant. The quantization is based on the…
We studied one-dimensional systems formed by $N$ identical particles confined in a harmonic trap and subject to an inverse power law interaction potential $\sim|x|^{-d}$. The correlation properties of a Wigner molecule with the lowest…
We investigate the ultraviolet behavior of 4-dimensional Lorentzian covariant Loop Quantum Gravity (LQG) and address the problem of infinite ambiguities relating to the triangulation dependence of spinfoam amplitudes. We consider the…
The longstanding open problem of approximating all singular vertex couplings in a quantum graph is solved. We present a construction in which the edges are decoupled; an each pair of their endpoints is joined by an edge carrying a $\delta$…
In this survey on combinatorial properties of triangulated manifolds we discuss various lower bounds on the number of vertices of simplicial and combinatorial manifolds. Moreover, we give a list of all known examples of vertex-minimal…
Consistent coupling of quantum and classical degrees of freedom exists so long as there is both diffusion of the classical degrees of freedom and decoherence of the quantum system. In this paper, we derive the Newtonian limit of such…
We consider the singular phases of the smooth finite-gap integrable systems arising in the context of Seiberg-Witten theory. These degenerate limits correspond to the weak and strong coupling regimes of SUSY gauge theories. The spectral…
The partition function of three dimensional gravity in the quantum regime is dual to the Ising model when the central charge $c=1/2$. Mathematically, we show that the three dimensional gravity can be described by Schramm-Loewner…
Euclidean quantum-gravity path-integrals are investigated within Regge calculus by computer simulations. The domain of integration is restricted by introducing a lower limit for the fatness of each simplex. We use the standard hypercubic…
We describe the idea of studying quantum gravity by means of dynamical triangulations and give examples of its implementation in 2, 3 and 4 space time dimensions. For $d=2$ we consider the generic hermitian 1-matrix model. We introduce the…
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…
We re-examine the nonperturbative curvature properties of two-dimensional Euclidean quantum gravity, obtained as the scaling limit of a path integral over dynamical triangulations of a two-sphere, which lies in the same universality class…
We present a possibility of coupling a point-like, non-singular, mass distribution to four-dimensional quantum gravity in the nonperturbative setting of causal dynamical triangulations (CDT). In order to provide a point of comparison for…
In the context of perturbative quantum field theory, the addition of quadratic-curvature invariants to the Einstein-Hilbert action makes it possible to achieve strict renormalizability in four dimensions. The additional terms $R^2$ and…
We discuss scaling relations in four dimensional simplicial quantum gravity. Using numerical results obtained with a new algorithm called ``baby universe surgery'' we study the critical region of the theory. The position of the phase…
A crucial requirement for the standard interpretation of Monte Carlo simulations of simplicial quantum gravity is the existence of an exponential bound that makes the partition function well-defined. We present numerical data favoring the…