Loop quantum gravity

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Loop quantum gravity (LQG), also known as loop gravity and quantum geometry, is a proposed quantum theory of spacetime which attempts to reconcile the theories of quantum mechanics and general relativity. Loop quantum gravity suggests that space can be viewed as an extremely fine fabric or network "woven" of finite quantised loops of excited gravitational fields called spin networks. When viewed over time, these spin networks are called spin foam, which should not be confused with quantum foam. A major quantum gravity contender with string theory, loop quantum gravity incorporates general relativity without requiring string theory's higher dimensions.

LQG preserves many of the important features of general relativity, while simultaneously employing quantization of both space and time at the Planck scale in the tradition of quantum mechanics. The technique of loop quantization was developed for the nonperturbative quantization of diffeomorphism-invariant gauge theory. Roughly, LQG tries to establish a quantum theory of gravity in which the very space itself, where all other physical phenomena occur, becomes quantized.

LQG is one of a family of theories called canonical quantum gravity. The LQG theory also includes matter and forces, but does not address the problem of the unification of all physical forces the way some other quantum gravity theories such as string theory do.

Contents

History of LQG

In 1986, Abhay Ashtekar reformulated Einstein's field equations of general relativity, using what have come to be known as Ashtekar variables, a particular flavor of Einstein-Cartan theory with a complex connection. In 1988, Carlo Rovelli and Lee Smolin used this formalism to introduce the loop representation of quantum general relativity, which was soon developed by Ashtekar, Rovelli, Smolin and many others. In the Ashtekar formulation, the fundamental objects are a rule for parallel transport (technically, a connection) and a coordinate frame (called a vierbein) at each point. Because the Ashtekar formulation was background-independent, it was possible to use Wilson loops as the basis for a nonperturbative quantization of gravity. Explicit (spatial) diffeomorphism invariance of the vacuum state plays an essential role in the regularization of the Wilson loop states.

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