Introduction to Loop Quantum Gravity

An Introduction to Loop Quantum Gravity and Its Application to Black Holes

This paper provides a brief introduction to Loop Quantum Gravity which is the main competitor of String Theory for a quantized theory of gravity. It is formulated on the basis of a Hamiltonian formalism of General Relativity with quantization performed in a non-perturbative and background independent manner. Coupling to matter fields as they appear in the Standard Model is also considered. Cano...

Covariant Loop Quantum Gravity An elementary introduction to Quantum Gravity and Spinfoam Theory

Loop Representations

The loop representation plays an important role in canonical quantum gravity because loop variables allow a natural treatment of the constraints. In these lectures we give an elementary introduction to (i) the relevant history of loops in knot theory and gauge theory, (ii) the loop representation of Maxwell theory, and (iii) the loop representation of canonical quantum gravity.

Quantum Gravity: General Introduction and Recent Develop- ments

I briefly review the current status of quantum gravity. After giving some general motivations for the need of such a theory, I discuss the main approaches in quantizing general relativity: Covariant approaches (perturbation theory, effective theory, and path integrals) and canonical approaches (quantum geometrodynamics, loop quantum gravity). I then address quantum gravitational aspects of stri...

Quantum isolated horizons and black hole entropy

We give a short introduction to the approaches currently used to describe black holes in loop quantum gravity. We will concentrate on the classical issues related to the modeling of black holes as isolated horizons, give a short discussion of their canonical quantization by using loop quantum gravity techniques, and a description of the combinatorial methods necessary to solve the counting prob...