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marcus

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A major change is happening in the way LQG is formulated.

Suzanne Lanery gave a seminar about this 5 days ago (10 Dec) at Perimeter, and today she gave a similar talk at Nijmegen (Renate Loll's seminar).

It's evident there is a lot of interest in this new development, which is based on the 11 November Lanery-Thiemann paper called

You can get the paper simply by googling

For the moment, at least, the first hit, searching with that googlekey, is

http://arxiv.org/abs/1411.3592

Suzanne Lanéry, Thomas Thiemann

(Submitted on 11 Nov 2014)

Instead of formulating the state space of a quantum field theory over one big Hilbert space, it has been proposed by Kijowski to describe quantum states as

...

If the gauge group happens to be compact, we also have at our disposal the well-established Ashtekar-Lewandowski Hilbert space, which is defined as an inductive limit using building blocks labeled by edges only. We then show that the quantum state space presented here can be thought as a natural extension of the space of density matrices over this Hilbert space. In addition, it is manifest from the classical counterparts of both formalisms that

81 pages, many figures

Suzanne Lanery gave a seminar about this 5 days ago (10 Dec) at Perimeter, and today she gave a similar talk at Nijmegen (Renate Loll's seminar).

It's evident there is a lot of interest in this new development, which is based on the 11 November Lanery-Thiemann paper called

**Projective LQG**You can get the paper simply by googling

**[projective LQG arxiv].**For the moment, at least, the first hit, searching with that googlekey, is

http://arxiv.org/abs/1411.3592

**Projective Loop Quantum Gravity I. State Space**Suzanne Lanéry, Thomas Thiemann

(Submitted on 11 Nov 2014)

Instead of formulating the state space of a quantum field theory over one big Hilbert space, it has been proposed by Kijowski to describe quantum states as

**projective families of density matrices over a collection of smaller, simpler Hilbert spaces**. Beside the physical motivations for this approach, it could help designing a quantum state space holding the states we need. .....

If the gauge group happens to be compact, we also have at our disposal the well-established Ashtekar-Lewandowski Hilbert space, which is defined as an inductive limit using building blocks labeled by edges only. We then show that the quantum state space presented here can be thought as a natural extension of the space of density matrices over this Hilbert space. In addition, it is manifest from the classical counterparts of both formalisms that

**the projective approach allows for a more balanced treatment of the holonomy and flux variables,**so it might pave the way for the development of more satisfactory coherent states.81 pages, many figures

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