Is the lack of infinities in LQG due to quantization of volume and area?

[zetafunction]

Why NO infinities in LQG ??

what is the reason for LQG in 4-dimension to have NO infinities when doing calculations ?? , is it due to the fact that the VOlume and Area operators are Quantizied ?

then if VOlume and Area are Quantizied, there should be a MINIMUM or quantum of area or volume we can detect and hence there would be a natural UV Cut-off , is this correct ??

by the way , a GOOD book to learn LQG ??, i have notions of SR , GR and Quantum mechanics... thanks.

 

[hamster143]

Exactly, There's a quantum of area and a quantum of volume, and they are both hard physical predictions of the theory. One problem is, they are so tiny (order of square and cube of Planck length) that they don't have many physical consequences.

There's a good book on LQG by Rovelli (it's not very recent, 2004, I think?), if you have access to a scientific library, check it out ... our scientific library had it. If not, there used to be a draft version available online, check it out.

 

[marcus]

https://www.physicsforums.com/showthread.php?p=2493787#post2493787

that has a link (halfway down page) to the draft of Rovelli's book
and also some more concentrated concise treatments by the same guy

some links in that post are broken, so I corrected them here:
https://www.physicsforums.com/showthread.php?p=2548572#post2548572

 

[humanino]

Another major LQG textbook writer, please let me know if you disagree, I think Rovelli and Thiemann are complementary in their approaches
Introduction to Modern Canonical Quantum General Relativity
(this is available for free, Thiemann also has a slightly more recent but slightly more expensive Cambridge Monographs with the same title).

 

[marcus]

Another major LQG textbook writer, please let me know if you disagree, I think Rovelli and Thiemann are complementary in their approaches
Introduction to Modern Canonical Quantum General Relativity
(this is available for free, Thiemann also has a slightly more recent but slightly more expensive Cambridge Monographs with the same title).

Thanks, humanino. I will revise the list of useful source links here
https://www.physicsforums.com/showthread.php?p=2493787#post2493787
so that it will include the link you suggest:
http://arxiv.org/abs/gr-qc/0110034
Introduction to Modern Canonical Quantum General Relativity (free 2001 draft version)

 

[hamster143]

Thiemann is probably smart and he knows what he's talking about, but I found his writing style remarkably dense, and he skips a lot of important background. Rovelli's text is written well enough that you can follow his logic all the way to the end of the book.