How Does Loop Quantum Gravity Approach Particle Scattering?

[marcus]

new today
http://arxiv.org/abs/gr-qc/0502036
Particle scattering in loop quantum gravity
Leonardo Modesto, Carlo Rovelli
4 pages

"We devise a technique for defining and computing n-point functions in the context of a background-independent gravitational quantum field theory. We construct a tentative implementation of this technique in a perturbatively-finite loop/spinfoam model."

 

[marcus]

Hmm some other new stuff today
what can this be about?
http://arxiv.org/abs/hep-th/0502092

Spin Foam Models of String Theory
Aleksandar Mikovic
6 pages, talk given at the Summer School in Modern Mathematical Physics, Zlatibor, 20-31 August, 2004

"We review briefly the spin foam formalism for constructing path integrals for the BF and related theories. Then we describe how the path integral for the string theory on a group manifold can be defined as a two-dimensional spin foam state sum."

can this be a sensible line of investigation? the last time someone tried to model string theory using loop-related methods there was a great rumpus

 

[marcus]

another new posting is a mainly mathematical contribution
from Jose Velhinho

http://arxiv.org/abs/gr-qc/0502038
Denseness of Ashtekar-Lewandowski states and a generalized cut-off in loop quantum gravity
J. M. Velhinho
15 pages

"We show that the set of states of the Ashtekar-Isham-Lewandowski holonomy algebra defined by elements of the Ashtekar-Lewandowski Hilbert space is dense in the space of all states. We consider weak convergence properties of a modified version of the cut-off procedure currently in use in loop quantum gravity. This version is adapted to vector states rather than to general distributions."

we have discussed other work by him at PF. this paper doesn't look revolutionary in any sense but is part of necessary masonry: like filling in the cracks

 

[marcus]

Well yesterday a paper by Rovelli and today one by John Barrett
(the Barrett-Crane model is the main type of spinfoam model that has been investigated so far. Barrett is inventive, so worth keeping track of)

http://arxiv.org/abs/gr-qc/0502048
Feynman diagams coupled to three-dimensional quantum gravity
John W. Barrett
7 pages

"A framework for quantum field theory coupled to three-dimensional quantum gravity is proposed. The coupling with quantum gravity regulates the Feynman diagrams. One recovers the usual Feynman amplitudes in the limit as the cosmological constant tends to zero."

this paper is a further development of one Barrett posted a couple of months ago:
http://arxiv.org/abs/gr-qc/0412107
Feynman loops and three-dimensional quantum gravity
John W. Barrett
14 pages

"This paper explores the idea that within the framework of three-dimensional quantum gravity one can extend the notion of Feynman diagram to include the coupling of the particles in the diagram with quantum gravity. The paper concentrates on the non-trivial part of the gravitational response, which is to the large momenta propagating around a closed loop. By taking a limiting case one can give a simple geometric description of this gravitational response. This is calculated in detail for the example of a closed Feynman loop in the form of a trefoil knot. The results show that when the magnitude of the momentum passes a certain threshold value, non-trivial gravitational configurations of the knot play an important role.
The calculations also provide some new information about a limit of the coloured Jones polynomial which may be of independent mathematical interest."

-------------
another one posted today that I cannot evaluate but want to keep track of is by John Klauder (whose work I don't know at all)
http://arxiv.org/abs/gr-qc/0502045
Elementary Model of Constraint Quantization with an Anomaly
J. Scott Little, John R. Klauder
14 pages, 2 figures

"Quantum gravity is made more difficult in part by its constraint structure. The constraints are classically first-class; however, upon quantization they become partially second-class. To study such behavior, we focus on a simple problem with finitely many degrees of freedom and demonstrate how the projection operator formalism for dealing with quantum constraints is well suited to this type of example."

Klauder's 15 papers go back to 1993 (when he co-authored with Jerzy Lewandowski). Here is a list
http://arxiv.org/find/gr-qc/1/au:+Klauder_J/0/1/0/all/0/1

 

[selfAdjoint]

Hmm some other new stuff today
what can this be about?
http://arxiv.org/abs/hep-th/0502092

Spin Foam Models of String Theory
Aleksandar Mikovic
6 pages, talk given at the Summer School in Modern Mathematical Physics, Zlatibor, 20-31 August, 2004

"We review briefly the spin foam formalism for constructing path integrals for the BF and related theories. Then we describe how the path integral for the string theory on a group manifold can be defined as a two-dimensional spin foam state sum."

can this be a sensible line of investigation? the last time someone tried to model string theory using loop-related methods there was a great rumpus

It's not too bad. He uses the term "spin foam" for any triangulation labeled by spin states, or more generally irreps of some group. He uses the "spin foam" to generate path integrals. He warms up by generating BF theory over a triangulated manifold pretty much following Baez. Then he does a bosonic string in flat spacetime, no prob. Finally he considers a string propagating on a group manifold. Here he has to use the dual of the triangulation which raises a problem. From his conlusion:

The sum (16) is a new type of the spin foam sum, and it differs from the usual one by the fact that the vertices of the dual 2-complex are labeled by the group irreps instead of the faces. In the dual picture this means that one labels the triangles of a triangulation, whose weights are given by the dimensions of the corresponding irreps, while the edges have weights as functions of the two triangle irreps who share that particular edge. As a result, the string theory state sum is different from the one coming from the 2d BF theory, and therefore it is not clear how the proposal made in [14], which was based on the 2d BF theory state sum, is related to the standard string theory.

Reference [14] is to a paper of his from a couple of years ago.