Loop Quantum Gravity

Abstract

Loop quantum gravity is an approach to the quantization of the gravitational field. It is an unusual quantum field theory in the sense that no classical geometry is used in the construction of its structures, such as operators, Hilbert spaces. Since the gravitational field endows spacetime with geometry, loop quantum gravity is also a theory of quantum spacetime geometry. A quasi atomistic picture of quantum geometry emerges, with small quanta of space making up macroscopic geometry. Transitions within these quanta of space, or regarding their arrangement can be thought of as evolution. We describe this picture and its origins, and we consider the unusual form, the dynamics takes in this theory. We close by describing some extensions of the formalism, such as inclusion of matter, reference systems, and an application to quantum cosmology.