Related papers: Two-Dimensional Lattice Gravity as a Spin System
The problem of fixing measure in the path integral for the Regge-discretised gravity is considered from the viewpoint of it's "best approximation" to the already known formal continuum general relativity (GR) measure. A rigorous formulation…
We study an Ising spin system coupled to a fluctuating four-dimensional $Z_2$-Regge lattice and compare with the results of the four-dimensional Ising model on a regular lattice. Particular emphasis is placed on the phase transition of the…
Lattice gauge theory is now well into its third decade as a major subfield of theoretical particle physics. I open these lattice sessions with a brief review of the motivations for this formulation of quantum field theory. I then comment on…
Recently, a new path integral formulation of Loop Quantum Gravity (LQG) has been derived in arXiv:1910.03763 from the reduced phase space formulation of the canonical LQG. This paper focuses on the semiclassical analysis of this path…
This is an informal review of the formulation of canonical general relativity and of its implications for quantum gravity; the various versions are compared, both in the continuum and in a discretized approximation suggested by Regge…
Algebraic systems called the local geodesic loops and their tangent Akivis algebras are considered. Their possible role in theory of gravity is considered. Quantum conditions for the infinitesimal quantum events are proposed.
The formulation of gravity in 3+1 dimensions in which the spin connection is the basic field ($\omega $-frame) leads to a theory with first and second class constraints. Here, the Dirac brackets for the second class constraints are…
We give a geometrical derivation of the Dirac equation by considering a spin-1/2 particle travelling with the speed of light in a cubic spacetime lattice. The mass of the particle acts to flip the multi-component wavefunction at the lattice…
This paper defines a notion of parallel transport in a lattice of quantum particles, such that the transformation associated with each link of the lattice is determined by the quantum state of the two particles joined by that link. We focus…
A major unsolved problem in theoretical physics is to reconcile the classical theory of general relativity with quantum mechanics. These lectures will deal with an attempt to describe quantum gravity as a path integral over geometries known…
We propose a new type of gauge in two-dimensional quantum gravity. We investigate pure gravity in this gauge, and find that the system reduces to quantum mechanics of loop length $l$. Furthermore, we rederive the $c\!=\!0$ string field…
We present a formulation of Regge Calculus where arbitrary coordinates are associated to each vertex of a simplicial complex and the degrees of freedom are given by the metric on each simplex. The lengths of the edges are thus determined…
The Wegner $Z_2$ gauge theory-$Z_2$ Ising spin model duality in $(2+1)$ dimensions is revisited and derived through a series of canonical transformations. The Kramers-Wannier duality is similarly obtained. The Wegner $Z_2$ gauge-spin…
Starting from an action for discretized gravity we derive a canonical formalism that exactly reproduces the dynamics and (broken) symmetries of the covariant formalism. For linearized Regge calculus on a flat background -- which exhibits…
We study the quantum dynamics of a charged particle in a two-dimensional lattice, subject to constant and homogeneous electric and magnetic fields. We find that different regimes characterize these motions, depending on a combination of…
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…
A model of two-dimensional quantum gravity that is the analog of the tensionless string is proposed. The gravitational constant ($k$) is the analog of the Regge slope ($\alpha^{'}$) and it shows that when $k \rightarrow \infty$, $2D$…
These lectures are intended for graduate students who want to acquire a working knowledge of path integral methods in a wide variety of fields in physics. In general the presentation is elementary and path integrals are developed in the…
Loop quantum gravity is a physical theory which aims at unifying general relativity and quantum mechanics. It takes general relativity very seriously and modifies it via a quantisation. General relativity describes gravity in terms of…
In this talk I review some of the recent developments in the field of random surfaces and the Dynamical Triangulation approach to simplicial quantum gravity. In two dimensions I focus on the c=1 barrier and the fractal dimension of…