I wasn't sure what you were asking, but it could be you would like a reference for why loop quantum gravity is UV-finite. This is basically a consequence of the theory being diffeomorphism invariant.I don't understand why a diffeomorphism invariance allows the extention of the loops variables in the continuum limit. Can someone give me some detailed reference?
There is a nice short formal proof of finiteness on page 281 of Rovelli's book.i was refering exactly to that talk for string theorists. In presenting loop variables, rovelli said that loop variables borns in lattice theories and in the general cases you can't extend loop variables in the continuum space limit but for diff invariant theories.
thank you very much.There is a nice short formal proof of finiteness on page 281 of Rovelli's book.
(I have the hardcover first edition). He also gives some intuitive explanation to help understand why the mathematical proof works, down at the bottom of page 281.
As he mentions on the top of page 277, the UV finiteness extends to matter fields defined on the LQG spin network, and he discusses this formally starting on page 289, section 7.3 "Matter: dynamics and finiteness"
You asked for some references to things to read. I don't want you to have to go and buy Rovelli's book! What we need to do is find out what page 281 corresponds to in the free-online early draft version.
The section we have to look for is called 7.1.1 "Finiteness". I think if we go back to the early draft version the page number will be different but probably the section number, 7.1.1, will be the same. At least the chapter order will be the same, so look in chapter 7.
To find the free downloadable 2003 draft version, google "Rovelli"
which will give you
and on that page you will find a link to the free copy.
Oh no! I just checked, and the link to the free copy has gone away! This presents a problem.
Whew! The book is still available free, here:
And the explanation you need is on page 202 (of the old draft version) in section 7.1.1
Check it out! He is a clear writer who puts in a lot of intuition.