Related papers: Loop Representations
We review the application of the loop representation to gauge theories and general relativity. The emphasis lies on exhibiting the loop calculus techniques, and their application to the canonical quantization. We discuss the role that knot…
As a canonical and generally covariant gauge theory, loop quantum gravity requires special techniques to derive effective actions or equations. If the proper constructions are taken into account, the theory, in spite of considerable…
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 a generalization of the first-order formalism used to describe the dynamics of a classical system. The generalization is then applied to the first-order action that describes General Relativity. As a result we obtain equations…
A new representation of Quantum Gravity is developed. This formulation is based on an extension of the group of loops. The enlarged group, that we call the Extended Loop Group, behaves locally as an infinite dimensional Lie group. Quantum…
Quantization of the system comprising gravitational, fermionic and electromagnetic fields is developed in the loop representation. As a result we obtain a natural unified quantum theory. Gravitational field is treated in the framework of…
We present an implementation of the loop representation of quantum gravity on a square lattice. Instead of starting from a classical lattice theory, quantizing and introducing loops, we proceed backwards, setting up constraints in the…
Quantization of the free Maxwell field in Minkowski space is carried out using a loop representation and shown to be equivalent to the standard Fock quantization. Because it is based on coherent state methods, this framework may be useful…
After a brief introduction to classical and quantum gravity we discuss applications of loop quantum gravity in the cosmological realm. This includes the basic formalism and recent results of loop quantum cosmology, and a computation of…
Since the gauge group underlying 2+1-dimensional general relativity is non-compact, certain difficulties arise in the passage from the connection to the loop representations. It is shown that these problems can be handled by appropriately…
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…
Most of the potential physical effects of loop quantum gravity have been derived in effective models that modify the constraints of canonical general relativity in specific forms. Emergent modified gravity evaluates important conditions…
We discuss the theory of knots, and describe how knot invariants arise naturally in gravitational physics. The focus of this review is to delineate the relationship between knot theory and the loop representation of non-perturbative…
A nonperturbative approach to quantum gravity that has generated much discussion is the attempt to construct a ``loop representation." Despite it's success in linear quantum theories and a part of 2+1 quantum gravity, it has recently been…
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…
The Gauss constraint in the extended loop representation for quantum gravity is studied. It is shown that there exists a sector of the state space that is rigorously gauge invariant without the generic convergence issues of the extended…
The canonical ``loop'' formulation of quantum gravity is a mathematically well defined, background independent, non perturbative standard quantization of Einstein's theory of General Relativity. Some among the most meaningful results of the…
We study the loop representation of the quantum theory for 2+1 dimensional general relativity on a manifold, $M = {\cal T}^2 \times {\cal R}$, where ${\cal T}^2$ is the torus, and compare it with the connection representation for this…
We give a standard introduction to loop quantum gravity, from the ADM variables to spin network states. We include a discussion on quantum geometry on a fixed graph and its relation to a discrete approximation of general relativity.
We describe the basic assumptions and key results of loop quantum gravity, which is a background independent approach to quantum gravity. The emphasis is on the basic physical principles and how one deduces predictions from them, at a level…