Lectures on non-perturbative canonical gravity


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Loop quantum gravity LQG , also known as loop gravity , quantum geometry and canonical quantum general relativity, is a proposed quantum theory of spacetime which attempts to blend together the seemingly incompatible theories of quantum mechanics and general relativity. This theory is one of a family of theories called canonical quantum gravity.

It was developed in parallel with loop quantization , a rigorous framework for nonperturbative quantization of diffeomorphism-invariant gauge theory. In plain english this is a quantum theory of gravity in which the very space that all other physics occurs in is quantized. This is not the most popular theory of quantum gravity and many physicist have big philosophical problems with it. For one thing the critics of this theory cite that it does not predict the existence of extra dimensions, does not predict the masses or charges of particles, etc; such as in String theory.

The rebuttal in general boils down to LQG being a theory of gravity and nothing more. In the view of those scientist who agree with LQG the facts that it does not predict any of those properties of particles are not a problem. There are many other theories of quantum gravity a list of them can be found on the Quantum gravity page. This very article has been subject of intense debate which can be found on the talk page Talk:Loop quantum gravity. LQG in itself was initially less ambitious than string theory, purporting only to be a quantum theory of gravity. String theory, on the other hand, appears to predict not only gravity but also various kinds of matter and energy that lie inside spacetime.

But this is not proven, and it is also not proven that the matter artifacts of string theory are exactly the same as observed matter.

Reading Guide to LQG

Should LQG succeed as a quantum theory of gravity, the known matter fields would have to be incorporated into the theory a posteriori. Lee Smolin , one of the fathers of LQG, has explored the possibility that string theory and LQG are two different approximations to the same ultimate theory.


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The main claimed successes of loop quantum gravity are: 1 that it is a nonperturbative quantization of 3-space geometry, with quantized area and volume operators; 2 that it includes a calculation of the entropy of black holes ; and 3 that it is a viable gravity-only alternative to string theory. However, these claims are not universally accepted.

While many of the core results are rigorous mathematical physics , their physical interpretations are speculative. LQG may or may not be viable as a refinement of either gravity or geometry; entropy is calculated for a kind of hole which may or may not be a black hole. It should be noted that several quantum gravity alternatives, such as spin foam , and causal dynamic triangulation are also sometimes called "loop quantum gravity".


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Main article: quantum gravity. Quantum field theory studied on curved non-Minkowskian backgrounds has shown that some of the core assumptions of quantum field theory cannot be carried over. In particular, the vacuum, when it exists, is shown to depend on the path of the observer through space-time see Unruh effect. Historically, there have been two reactions to the apparent inconsistency of quantum theories with the necessary background-independence of general relativity. The first is that the geometric interpretation of general relativity is not fundamental, but emergent.

The other view is that background-independence is fundamental, and quantum mechanics needs to be generalized to settings where there is no a priori specified time. Loop quantum gravity is an effort to formulate a background-independent quantum theory. Main article: history of loop quantum gravity. In physicist 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.

He was able to quantize gravity using gauge field theory. 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.

Around , Carlo Rovelli and Lee Smolin obtained an explicit basis of states of quantum geometry, which turned out to be labelled by Penrose's spin networks. In this context, spin networks arose as a generalization of Wilson loops necessary to deal with mutually intersecting loops. Mathematically, spin networks are related to group representation theory and can be used to construct knot invariants such as the Jones polynomial.

Lectures on Non-Perturbative Canonical Gravity

Being closely related to topological quantum field theory and group representation theory, LQG is mostly established at the level of rigour of mathematical physics. Open to the public ; Monash University Library. The University of Melbourne Library. University of Queensland Library. Open to the public ; QC Barr Smith Library.

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Spin networks, spin foams and loop quantum gravity

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Lectures on non-perturbative canonical gravity Lectures on non-perturbative canonical gravity
Lectures on non-perturbative canonical gravity Lectures on non-perturbative canonical gravity
Lectures on non-perturbative canonical gravity Lectures on non-perturbative canonical gravity
Lectures on non-perturbative canonical gravity Lectures on non-perturbative canonical gravity
Lectures on non-perturbative canonical gravity Lectures on non-perturbative canonical gravity
Lectures on non-perturbative canonical gravity Lectures on non-perturbative canonical gravity

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