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marcus

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**Loop gravity Hamiltonian---for Jeff and/or Eigenguy**

Sources on the loop gravity Hamiltonian would include, I guess, these two sections of Rovelli's textbook "Quantum Gravity"

**Chapter 4 Hamiltonian General Relativity**pages 97-108

especially section 4.1.2 "The Hamilton function of GR and its physical meaning"

(in classical GR the physical meaning of the hamilton function is not what one has learned to expect, due to differences in definitions of energy and time)

**Chapter 7 Quantum Spacetime: the Hamiltonian Operator**pages 167-174

At different time both Jeff and Eigenguy have been asking along similar lines about the loop gravity Hamiltonian and have cited the same article by Thiemann---who around 1996/1997 constructed a form of the Hamiltonian with which almost immediately Lewandowski pointed out problems. This had repercussions.

On 30 October, actually just in a few days, Lewandowski will give a talk on the Hamiltonian of quantum gravity at the "Strings meets Loops" symposium near Berlin. If the talk is posted, it may give an authoritative view for a wide audience.

Also since Rovelli's textbook is intended an introductory graduate level text to a fairly new subject matter it is, at least in places, fairly accessible---not too heavily technical. At least worth a look since Rovelli generally has a realistic down-to-earth approach.

There are two different issues involved----the second, and less important I think, is Thiemann's trouble with his construction of the constraint and the unhappy consequences which he doubtless still feels. The first as I see it, is already latent in GR, and you get a taste of it in Rovelli's Dialog on page 17. I will type in an exerpt

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