相关论文: Random Surfaces and Lattice Gravity
The main results for the two-dimensional quantum gravity, conjectured from the matrix model or integrable approach, are presented in the form to be compared with the world-sheet or Liouville approach. In spherical limit the integrable side…
We study "random surfaces," which are random real (or integer) valued functions on Z^d. The laws are determined by convex, nearest neighbor, difference potentials that are invariant under translation by a full-rank sublattice L of Z^d; they…
Causal Dynamical Triangulations (CDT) is a methodology to define and compute the gravitational path integral, whose aim is a fully fledged nonperturbative quantum field theory of gravity and spacetime. Analogous to lattice formulations of…
Four-dimensional CDT (causal dynamical triangulations) is a lattice theory of geometries which one might use in an attempt to define quantum gravity non-perturbatively, following the standard procedures of lattice field theory. Being a…
We discuss some problems related to dimensional reductions of gravity theories to two-dimensional and one-dimensional dilaton gravity models. We first consider the most general cylindrical reductions of the four-dimensional gravity and…
We look over recent developments on our understanding about relativistic matter under external electromagnetic fields and mechanical rotation. I review various calculational approaches for concrete physics problems, putting my special…
We present an overview of recent developments concerning modifications of the geometry of space-time to describe various physical processes of interactions among classical and quantum configurations. We concentrate in two main lines of…
Each approach to the quantum-gravity problem originates from expertise in one or another area of theoretical physics. The particle-physics perspective encourages one to attempt to reproduce in quantum gravity as much as possible of the…
We propose a computation of curvature of arbitrary two-dimensional surfaces of three-dimensional objects, which is a contribution to discrete gravity with potential applications in network geometry. We begin by linking each point of the…
This PhD thesis deals with a number of different problems in mathematical physics with the common thread that they have probabilistic aspects. The problems all stem from mathematical studies of lattice systems in statistical and quantum…
Motivated by the search for new observables in nonperturbative quantum gravity, we consider Causal Dynamical Triangulations (CDT) in 2+1 dimensions with the spatial topology of a torus. This system is of particular interest, because one can…
We consider a new action of a two-dimensional field theory interacting with gravitational field. The action is interpreted as the area of a surface imbedded into four-dimensional Mincowski target space. In addition to reparametrization…
Two dimensional flows on fixed smooth surfaces have been studied in the point of view of vorticity dynamics. Firstly, the related deformation theory including kinematics and kinetics is developed. Secondly, some primary relations in…
The problem of a periodic scalar field on a two-dimensional dynamical random lattice is studied with the inclusion of vortices in the action. Using a random matrix formulation, in the continuum limit for genus zero surfaces the partition…
This paper deals with a detail study of gravitational collapse of dust and viscous fluids under the assumptions of spherical symmetry. Our main goal is to closely analyze the horizons which arise during this gravitational phenomenon. To…
We extend a model of four-dimensional simplicial quantum gravity to include degenerate triangulations in addition to combinatorial triangulations traditionally used. Relaxing the constraint that every 4-simplex is uniquely defined by a set…
The Causal Dynamical Triangulation (CDT) approach to quantum gravity is a lattice approximation to the gravitational path integral. Developed by Ambj\o{}rn, Jurkiewicz and Loll, it has yielded some important results, notably the emergence…
We do not yet know how to quantize gravity in 3+1 dimensions, but in lower dimensions we face the opposite problem: many of the approaches originally developed for (3+1)-dimensional gravity can be successfully implemented in 2+1 dimensions,…
Based on a combinatorial approach and random matrix theory, we show a central limit theorem that gives important insight into causally triangulated $3d$ quantum gravity.
A number of recent proposals for a quantum theory of gravity are based on the idea that spacetime geometry and gravity are derivative concepts and only apply at an approximate level. There are two fundamental challenges to any such…