Related papers: Knot theory and quantum gravity in loop space: a p…
General relativity successfully describes space-times at scales that we can observe and probe today, but it cannot be complete as a consequence of singularity theorems. For a long time there have been indications that quantum gravity will…
The recently proposed loop representation, used previously to find exact solutions to the quantum constraints of general relativity, is here used to quantize linearized general relativity. The Fock space of graviton states and its…
The quantum gravity is formulated based on principle of local gauge invariance. The model discussed in this paper has local gravitational gauge symmetry and gravitational field is represented by gauge field. In leading order approximation,…
Since the early days of search for a quantum theory of gravity the attempts have been mostly concentrated on the quantization of an otherwise classical system. The two most contentious candidate theories of gravity, sting theory and quantum…
In recent years, Loop Quantum Gravity has emerged as a solid candidate for a nonperturbative quantum theory of General Relativity. It is a background independent theory based on a description of the gravitational field in terms of…
Important characteristics of the loop approach to quantum gravity are a specific choice of the algebra A of observables and of a representation of A on a measure space over the space of generalized connections. This representation is…
We present an introduction to the canonical quantization of gravity performed in loop quantum gravity, based on lectures held at the 3rd quantum geometry and quantum gravity school in Zakopane in 2011. A special feature of this introduction…
..."but we do not have quantum gravity." This phrase is often used when analysis of a physical problem enters the regime in which quantum gravity effects should be taken into account. In fact, there are several models of the gravitational…
I propose a new mathematical form for the quantum theory of gravity coupled to matter. The motivation is from the connection between CSW TQFT and the Ashtekar variables. I also connect the algebraic structure of TQFT with some thoughts…
An introduction to loop quantum gravity is given, focussing on the fundamental aspects of the theory, different approaches to the dynamics, as well as possible future directions. It is structured in five lectures, including exercises, and…
We summarize recent developments at the interface of quantum gravity and quantum information, and discuss applications to the quantum geometry of space in loop quantum gravity. In particular, we describe the notions of link entanglement,…
I present a summary of the recent progress made in field and string theory which has led to a reformulation of quantum-group polynomial invariants for knots and links into new polynomial invariants whose coefficients can be described in…
Over the last two decades, many unexpected relations between exotic smoothness, e.g. exotic $\mathbb{R}^{4}$, and quantum field theory were found. Some of these relations are rooted in a relation to superstring theory and quantum gravity.…
A pedagogical introduction to some of the main ideas and results of field theories on quantized spacetimes is presented, with emphasis on what such field theories may teach us about the problem of quantizing gravity. We examine to what…
We study three-dimensional Chern-Simons theory with complex gauge group SL(2,C), which has many interesting connections with three-dimensional quantum gravity and geometry of hyperbolic 3-manifolds. We show that, in the presence of a single…
General relativity has previously been extended to incorporate degenerate metrics using Ashtekar's hamiltonian formulation of the theory. In this letter, we show that a natural alternative choice for the form of the hamiltonian constraints…
This is the written version of a lecture given at the ``VI Mexican School of Gravitation and Mathematical Physics" (Nov 21-27, 2004, Playa del Carmen, Mexico), introducing the basics of Loop Quantum Geometry. The purpose of the written…
A phenomenology for the deep spatial geometry of loop quantum gravity is introduced. In the context of a simple model, an atom of space, it is shown how purely combinatorial structures can affect observations. The angle operator is used to…
The goal of this article is to present an introduction to loop quantum gravity -a background independent, non-perturbative approach to the problem of unification of general relativity and quantum physics, based on a quantum theory of…
This is the first in a series of papers outlining an algorithm to explicitly construct finite quantum states of the full theory of gravity in Ashtekar variables. The algorithm is based upon extending some properties of a special state, the…