Merging NCG matter with Spinfoam LQG spacetime (new Pfaeffle-Stephan)

[marcus]

This thread is in case discussion of the following paper is wished.
http://arxiv.org/abs/1102.0954
The Holst Action by the Spectral Action Principle
Frank Pfaeffle, Christoph A. Stephan
11 pages
(Submitted on 4 Feb 2011)
"We investigate the Holst action for closed Riemannian 4-manifolds with orthogonal connections. For connections whose torsion has zero Cartan type component we show that the Holst action can be recovered from the heat asymptotics for the natural Dirac operator acting on left-handed spinor fields."

(If anyone is coming in new to this, Holst action is the action used in Spinfoam LQG and Spectral Action Principle means they are talking Connes NC geometry realization of standard model matter. The title indicates they want to put Connes-style standard model matter together with LQG, which in fact is where they are going in the paper. They reference the standard LQG books Rovelli and Thiemann, and basic Connes and Chamseddine NCG papers about standard model matter. It seems to me that Pfaeffle and Stephan are trying to do something like what John Barrett was saying should be done in his January 2011 paper.)

In post #1410 of the QG bibliography I logged a paper by John Barrett, "Induced standard model and unification" which has now been given a new title:
http://arxiv.org/abs/1101.6078
State sum models, induced gravity and the spectral action
John W. Barrett
13 pages
(Submitted on 31 Jan 2011)
"A proposal that the bosonic action of the standard model is induced from the fermionic action is investigated. It is suggested that this might occur naturally in state sum models."

 

[marcus]

This paper puts Prof. Christian Bär on the map for me:
http://geometrie.math.uni-potsdam.de/index.php/de/mitarbeiter/prof-dr-christian-baer

Dr Pfaeffle and Dr Stephan are researchers at the Math Institiute at Uni Potsdam.
Prof. Bär is the senior geometry guy at the Math Institute. He has more papers and has been there longer. The two newer members have co-authored with him---now they are doing significant work on their own.

I will add all three to my list of people to watch out for.

Christoph Stephan lists his interests here:
http://geometrie.math.uni-potsdam.de/index.php/de/mitarbeiter/dr-christoph-stephan

• Nichtkommutative Geometrie
• Diracoperatoren in der Physik
• Elementarteilchenphysik

http://geometrie.math.uni-potsdam.de/index.php/de/mitarbeiter/dr-christoph-stephan/profil

It is nice to see the German establishment gear up for QG research at the University level. Like establishing a LQG group at Erlangen headed by Thiemann, a year or so ago.
Before, like 2 or more years ago, the activity was concentrated at Hermann Nicolai's branch of Max Planck Institute---at a special MPI QG branch, not at teaching institutions.
Now Sahlmann is at Karlsruhe, Thiemann is at Erlangen with a whole new group of postdocs, and Nicolai is hosting another generation (Oriti, Dittrich...) at the MPI. Gradually things grow and change.

 

[nicoo]

http://arxiv.org/abs/1105.0194
From Quantum Gravity to Quantum Field Theory via Noncommutative Geometry
Johannes Aastrup, Jesper M. Grimstrup
(Submitted on 1 May 2011)
"A link between canonical quantum gravity and fermionic quantum field theory is established in this paper. From a spectral triple construction which encodes the kinematics of quantum gravity semi-classical states are constructed which, in a semi-classical limit, give a system of interacting fermions in an ambient gravitational field. The interaction involves flux tubes of the gravitational field. In the additional limit where all gravitational degrees of freedom are turned off, a free fermionic quantum field theory emerges."

 

[marcus]

Nicoo, thanks for mentioning that paper.
You may have noticed that one of the authors, Jesper Grimstrup, is presenting their results this month at the Loops 2011 conference:
http://loops11.iem.csic.es/loops11/index.php?option=com_content&view=article&id=100%3Ajesper-grimstrup-coupling-matter-to-quantum-gravity-via-noncommutative-geometry&catid=36%3Aparallel-sesions&Itemid=73

Coupling Matter to Quantum Gravity via Noncommutative Geometry.
Jesper Grimstrup
CFMAC Room. Tuesday, May, 24th, 15:05 - 15:25.
Abstract:
In my talk I will show that elements of fermionic quantum field theory emerge from a geometrical construction over a configuration space of connections. The construction is a spectral triple - the key object in a noncommutative geometry - and it is built over an algebra of holonomy loops. The spectral triple encodes the kinematics of quantum gravity. It turns out that the spectral triple involves a natural class of semi-classical states which, in a semi-classical approximation, gives a system of interacting fermions. Furthermore, in the approximation where all gravitational degrees are "turned off" a free fermionic quantum field theory emerges. Thus, the spectral triple establishes a direct link between canonical quantum gravity and fermionic quantum field theory.

 

[nicoo]

Thanks Marcus for the info. That conference definitively looks interesting :)