Here's the paper I learned something like this from:
On the concept of determinant for the differential operators of Quantum Physics http://arxiv.org/abs/hep-th/9906229"
It requires using the zeta trace of the function (i.e. \zeta(s)=\sum_{n}\lambda_{n}^{-s}) when you take it's derivative...
I would suspect perhaps because these are the Casimir operators of the group? Just a wild guess, I don't have a copy of Halzen Martin's book or work or am I able to find a relevant quote :(
I think this is a vast understatement of the Veneziano amplitudes, which were used to explain Regge Trajectories and involved (dare I use the pun -- entangled?) with the Strong Force...or more precisely, "gluon fluxtubes" (a sort of proto-string object).
It's fascinating stuff, so I'll give...
Two ways: one is the sum over histories approach which requires knowledge only of the Lagrangian.
The other is to treat the potential A as the "position" coordinate, so we can find the canonically conjugate momenta
\pi = \frac{\partial L}{\partial \dot{A}}
and then use the Legendre...
I thought I made it perfectly clear that I don't believe that quantum mechanics is consistent with general relativity and needs to be modified in order to quantize general relativity.
But the weak field approximation doesn't always work when quantizing a system.
For example, if you look this...
Marcus:
Haha we need to coordinate better is all! :-p
Don't hesitate to give your two cents, I (more than likely) see things far differently than you do so you may have something to add that I overlooked.
And my cold is getting better, thanks for your concern :smile:
jimgraber: best of...
Just a historical background, String theory was originally invented to solve the problem of Strong force. It turned out to be wrong, and they re-applied it to other problems (the foundation of particle physics as a theory of everything, for example).
String theory was one of the approaches that...
Perhaps I should try to explain the background of QM more fully to justify my explanation.
You have a "phase space" in classical mechanics where the state of a classical body is described by a 2*D dimensional vector for D spatial dimensions and D "conjugate" momentum dimensions. So that's in...
Personally I think this is relatively narrow position (no offense)..."it's either gravitons or else you don't adequately believe in Planck's constant and gravitational waves" is too much of a false dilemma in my opinion.
What about the geon concept proposed by Wheeler? This is based on the...
I don't know if I agree with that last idea "quantum mechanics establishes a relationship between the metric and the measure" because the position eigenvectors you are using are defined on a Hilbert space...not "real" spacetime.
On the Hilbert space, the eigenvectors for position are...
I'm (obviously) not Marcus, but I feel compelled to intervene here because I firmly disbelieve in the graviton.
Have you looked up group field theoretic quantum gravity? It begins with one of its premises being there are no gravitons.
It was previously discussed on this forum as a matter...
I don't think so, but there was a rough draft on arxiv.org if memory serves. (I just looked it up, and it's An Introduction to Modern Canonical Quantum General Relativity, similar title but I think it's more of a scaffolding for the topics to cover in the book rather than a rough draft.)
The...
I think you'd find the mental stamina if you were sick and had nothing else to do all day ;)
Heck, my cold is so bad I sleep only a few hours at night. More time to study this fantastic text!
The book is very mathematical, but unlike your average "high level" math textbook Thiemann can...
I stumbled upon the book by accident when browsing at the UC Davis Library yesterday when I was trying to buy printer paper. I couldn't hold back, I bought the book and http://angryphysicist.wordpress.com/2007/11/15/thomas-thiemanns-modern-canonical-quantum-general-relativity/" of it (or what...