- #1

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Has research in LQG led to any breakthrough in mathematics or any mathematical new result so far?

- Thread starter Macuario
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- #1

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Has research in LQG led to any breakthrough in mathematics or any mathematical new result so far?

- #2

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- #3

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I wonder if there has been any advance in mathematics thanks to LQG. To the best of my knowledge that is not the case, and in fact LQG is regarded by mathematicians as completely uninteresting.

- #4

haushofer

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How mathematically well-defined is LQG anyway? Or something like the Wheeler-deWitt equation?

- #5

martinbn

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Probably as well as many other things in physics. How well-defined is the path integral? But it surely has been important to mathematicians.How mathematically well-defined is LQG anyway?

- #6

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- Development of spinnetwork theory (recoupling theory on a graph)

Has research in LQG led to any breakthrough in mathematics or any mathematical new result so far?

- Developments in twistor theory

- Hamiltonian mechanics of covariant systems (Littlejohn)

- Diff invariant gauge theories on a lattice

- The measure on diff invariant space(ashtekar-Lewandowski measure)

- Generalization of Perelomov coherent states on a lattice (Livine-Speziale CS)

- Twisted geometries as discretization of GR

- Mapping between 3d Chern-Simons theory and 4d simplicial geometry (Han-Haggard-Riello-Kaminski)

...just the first things that come to my mind...

Lack of interest just denote a lack of knowledge. By the way, many researchers doing LQG are based in Mathematical Departments. Because the work of developing LQG deals a lot with some nice mathematics.I wonder if there has been any advance in mathematics thanks to LQG. To the best of my knowledge that is not the case, and in fact LQG is regarded by mathematicians as completely uninteresting.

Having said all this, however, one must remark that nowadays the declared ambition of strings is mostly to contribute to mathematics or to condensed matter. While the ambition of LQG is to understand what happens to quantum spacetime: physics, not math.

Cheers,

f

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