Related papers: Noncomputability Arising In Dynamical Triangulatio…
Random tensor models can be used as combinatorial devices to generate Euclidean dynamical triangulations. A physical continuum limit of dynamical triangulations requires a suitable generalization of the double-scaling limit of random…
We explore an extended coupling constant space of 4d regularized Euclidean quantum gravity, defined via the formalism of dynamical triangulations. We add a measure term which can also serve as a generalized higher curvature term and…
The four dimensional Causal Dynamical Triangulations (CDT) approach to quantum gravity is already more than ten years old theory with numerous unprecedented predictions such as non-trivial phase structure of gravitational field and…
Quantum field theory provides the framework for the most fundamental physical theories to be confirmed experimentally and has enabled predictions of unprecedented precision. However, calculations of physical observables often require great…
Four-dimensional random geometries can be generated by statistical models with rank-4 tensors as random variables. These are dual to discrete building blocks of random geometries. We discover a potential candidate for a continuum limit in…
Quantum invariants in low dimensional topology offer a wide variety of valuable invariants of knots and 3-manifolds, presented by explicit formulas that are readily computable. Their computational complexity has been actively studied and is…
Models for topological quantum computation are based on braiding and fusing anyons (quasiparticles of fractional statistics) in (2+1)-D. The anyons that can exist in a physical theory are determined by the symmetry group of the Hamiltonian.…
A unified theory of four-dimensional gravity together with the standard model is presented, with supersymmetry breaking of M-theory at a TeV. Masses of the the known particles are derived. The cosmological constant is quantum generated to…
Interesting data often concentrate on low dimensional smooth manifolds inside a high dimensional ambient space. Random projections are a simple, powerful tool for dimensionality reduction of such data. Previous works have studied bounds on…
The causal dynamical triangulations approach aims to construct a quantum theory of gravity as the continuum limit of a lattice-regularized model of dynamical geometry. A renormalization group scheme--in concert with finite size scaling…
Starting with the irreducible triangulations of a fixed surface and splitting vertices, all the triangulations of the surface up to a given number of vertices can be generated. The irreducible triangulations have previously been determined…
We study numerically the dynamical triangulation formulation of two-dimensional quantum gravity using a restricted class of triangulation, so-called minimal triangulations, in which only vertices of coordination number 5, 6, and 7 are…
In topological quantum computation the geometric details of a particle trajectory are irrelevant; only the topology matters. Taking this one step further, we consider a model of computation that disregards even the topology of the particle…
In this note, we provide a unifying framework to investigate the computational complexity of classical spin models and give the full classification on spin models in terms of system dimensions, randomness, external magnetic fields and types…
We review some recent attempts to extract information about the nature of quantum gravity, with and without matter, by quantum field theoretical methods. More specifically, we work within a covariant lattice approach where the individual…
We conclude the construction of the algebraic complex, consisting of spaces of differentials of Euclidean metric values, for four-dimensional piecewise-linear manifolds. Assuming that the complex is acyclic, we investigate how its torsion…
The aim of the causal dynamical triangulations approach is to define nonperturbatively a quantum theory of gravity as the continuum limit of a lattice-regularized model of dynamical geometry. My aim in this paper is to give a concise yet…
We investigate quantum gravity in four dimensions using the Regge approach on triangulations of the four-torus with general, non-regular incidence matrices. We find that the simplicial lattice tends to develop spikes for vertices with low…
The statistical properties of dynamically triangulated manifolds (DT mfds) in terms of the geodesic distance have been studied numerically. The string susceptibility exponents for the boundary surfaces in three-dimensional DT mfds were…
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…