The issue of the dynamics is perhaps the central problem in canonical quantization approaches to totally constrained theories like quantum general relativity. There are three salient aspects of the problem that have prevented from advancing in the quantization. The first one is how to construct a space of physical states for the theory that are annihilated by the quantum constraints and that is endowed with a proper Hilbert space structure. The second issue is related to the introduction of a correspondence principle with the classical theory, in particular to check the constraint algebra at a quantum level. The third problem is how to address the ``problem of time'' that is, to introduce a satisfactory picture for the dynamics of the theory in terms of observable quantities.
Then come three pages of semi-technical stuff (finite number of degrees of freedom models, Legendre transformations) and eventually
Summarizing, the method of uniform discretizations allows to tackle
satisfactorily the three central problems of the dynamics of quantum
general relativity and provides new avenues for studying numerically
classical relativity as well.
Well done, guys! Now we can stop worrying about quantum gravity and spend all your energies to cheer up Klinsi's Jungs!
Sorry, I didn't have anything more intelligent to say.
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4 comments:
The paper did not help the German team ...
But they do state (near the end) "The only major hurdle that could stand in the way is that the continuum limit may not exist ..."
By the way 'abs' and 'gr-qc' in the link
http://arxiv.org/abs/gr-qc/0606121
is mixed up in your text.
Fixed the link, couldn't fix the football result.
read the same paper. thought the same thing. also have nothing more intelligent to say.
Gambini and Pullin are not unknow figures in Gravity research, they were heavily involved in early LQG.
Their discretization contains some (one) highly nontrivial aspects which they do not really make clear in that paper.
Basically what they do is create a single internal time parameter. Relative to the the kinematical states are the states that evolve, and you can define a probability distribution and so on.
This is nontrivial in so far as one would assume that in a system with more then one cosntraint one would require more then one time.
Essentially though it of course doesn't solve any of the conceptional or computational problems, because the parameter they introduce is unphysical, and is deeply entangled in their "sollution" of the problem of time/dynamics.
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