#### marcus

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Interesting development. We already knew nonstring QG at UC Davis, but hadn't heard of LQG research in the UC Berkeley physics department.

The acknowledgements thanked Rovelli among others, for discussions and hospitality---at least one of the authors must have visited Marseille and Pavia* while doing the research.

The senior author is Robert Littlejohn, impressive guy

http://physics.berkeley.edu/index.php?option=com_dept_management&act=people&Itemid=299&task=view&id=478

"Robert Littlejohn received his B.A. in 1975 and his Ph.D. in 1980, both from the University of California at Berkeley. After postdoctoral positions at the La Jolla Institute and the University of California, Los Angeles, he joined the Berkeley faculty in 1983. He has been a Presidential Young Investigator and a Miller Professor, and he is a fellow of the American Physical Society."

Now full professor at Berkeley best known for research in Plasma Physics And

http://www.physics.berkeley.edu/research/faculty/littlejohn.html [Broken]

MTd2 spotted the paper by Littlejohn and Haggard (PhD student working with Littlejohn):

http://arxiv.org/abs/0912.5384

Hal M. Haggard, Robert G. Littlejohn

(Submitted on 29 Dec 2009)

"We present the asymptotic formula for the Wigner 9j-symbol, valid when all quantum numbers are large, in the classically allowed region. As in the Ponzano-Regge formula for the 6j-symbol, the action is expressed in terms of lengths of edges and dihedral angles of a geometrical figure, but the angles require care in definition. Rules are presented for converting spin networks into the associated geometrical figures. The amplitude is expressed as the determinant of a 2x2 matrix of Poisson brackets. The 9j-symbol possesses caustics associated with the fold and elliptic and hyperbolic umbilic catastrophes. The asymptotic formula obeys the exact symmetries of the 9j-symbol."

http://compassproject.berkeley.edu/bio.php?profile=hal [Broken]

Here is how their paper starts out:

"The asymptotic behavior of spin networks has played a signiﬁcant role in simplicial approaches to quantum gravity. Indeed, the ﬁeld began with the observation that the Ponzano-Regge action(1968) for the semiclassical 6j-symbol is identical to the Einstein-Hilbert action of a tetrahedron in 3-dimensional gravity in the Regge formulation (Regge, 1961;...)

...

...In this article we present the generalization of the Ponzano-Regge formula to the Wigner 9j-symbol, as well as some material relevant for the asymptotics of arbitrary spin networks..."

*Pavia, see article "Quantum Tetrahedra" http://pubs.acs.org/doi/abs/10.1021/jp909824h

The acknowledgements thanked Rovelli among others, for discussions and hospitality---at least one of the authors must have visited Marseille and Pavia* while doing the research.

The senior author is Robert Littlejohn, impressive guy

http://physics.berkeley.edu/index.php?option=com_dept_management&act=people&Itemid=299&task=view&id=478

"Robert Littlejohn received his B.A. in 1975 and his Ph.D. in 1980, both from the University of California at Berkeley. After postdoctoral positions at the La Jolla Institute and the University of California, Los Angeles, he joined the Berkeley faculty in 1983. He has been a Presidential Young Investigator and a Miller Professor, and he is a fellow of the American Physical Society."

Now full professor at Berkeley best known for research in Plasma Physics And

**Nonlinear Dynamics**. Here is a page on his research interests:http://www.physics.berkeley.edu/research/faculty/littlejohn.html [Broken]

MTd2 spotted the paper by Littlejohn and Haggard (PhD student working with Littlejohn):

http://arxiv.org/abs/0912.5384

**Asymptotics of the Wigner 9j symbol**Hal M. Haggard, Robert G. Littlejohn

(Submitted on 29 Dec 2009)

"We present the asymptotic formula for the Wigner 9j-symbol, valid when all quantum numbers are large, in the classically allowed region. As in the Ponzano-Regge formula for the 6j-symbol, the action is expressed in terms of lengths of edges and dihedral angles of a geometrical figure, but the angles require care in definition. Rules are presented for converting spin networks into the associated geometrical figures. The amplitude is expressed as the determinant of a 2x2 matrix of Poisson brackets. The 9j-symbol possesses caustics associated with the fold and elliptic and hyperbolic umbilic catastrophes. The asymptotic formula obeys the exact symmetries of the 9j-symbol."

http://compassproject.berkeley.edu/bio.php?profile=hal [Broken]

Here is how their paper starts out:

"The asymptotic behavior of spin networks has played a signiﬁcant role in simplicial approaches to quantum gravity. Indeed, the ﬁeld began with the observation that the Ponzano-Regge action(1968) for the semiclassical 6j-symbol is identical to the Einstein-Hilbert action of a tetrahedron in 3-dimensional gravity in the Regge formulation (Regge, 1961;...)

...

...In this article we present the generalization of the Ponzano-Regge formula to the Wigner 9j-symbol, as well as some material relevant for the asymptotics of arbitrary spin networks..."

*Pavia, see article "Quantum Tetrahedra" http://pubs.acs.org/doi/abs/10.1021/jp909824h

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