marcus said:
Atyy has added a handful of ideas to the list I gave earlier of what might turn out to be the main themes of the conference...
...
...Another main theme, I mentioned A-D so this would be E: The more central role now being played by SUq(2).
The quantum version of SU(2) always used to be speculated about but it never seemed as central to Loop research as in the past year or so.
About SU
q, and also the q-deformed version of the Lorentz cover SL(2,C), it has appeared in many of the recent Loop papers. Including this by Wolfgang Wieland
http://arxiv.org/abs/1105.2330
but also these by Muxin Han and Bianchi Rovelli:
==quote==
http://arxiv.org/abs/1105.2212
Cosmological Constant in LQG Vertex Amplitude
Muxin Han
(Submitted on 11 May 2011)
A new q-deformation of the Euclidean EPRL/FK vertex amplitude is proposed by using the evaluation of the Vassiliev invariant associated with a 4-simplex graph (related to two copies of quantum SU(2) group at different roots of unity). We show that the large-j asymptotics of the q-deformed vertex amplitude gives the Regge action with cosmological constant (in the corresponding 4-simplex). In the end we also discuss its relation with a Chern-Simons theory on the boundary of 4-simplex.
http://arxiv.org/abs/1105.1898
A note on the geometrical interpretation of quantum groups and non-commutative spaces in gravity
Eugenio Bianchi, Carlo Rovelli
(Submitted on 10 May 2011)
Quantum groups and non-commutative spaces have been repeatedly utilized in approaches to quantum gravity. They provide a mathematically elegant cut-off, often interpreted as related to the Planck-scale quantum uncertainty in position. We consider here a different geometrical interpretation of this cut-off, where the relevant non-commutative space is the space of directions around any spacetime point. The limitations in angular resolution expresses the finiteness of the angular size of a Planck-scale minimal surface at a maximum distance 1/\sqrt{\Lambda} related the cosmological constant Lambda.
This yields a simple geometrical interpretation for the relation between the quantum deformation parameter
q=e^{i \Lambda l_{Planck}^2}
and the cosmological constant, and resolves a difficulty of more conventional interpretations of the physical geometry described by quantum groups or fuzzy spaces.
Comments: 2 pages, 1 figure
==endquote==
Wieland, Han, Bianchi, and Rovelli are all in the Marseille group. What it looks like is that everything in Loop gravity coming out of that research team involves the quantum group---either as an approach to renormalization (getting convergence) or to including the positive cosmological constant (accelerated cosmic expansion: deSitter as opposed to Anti-deSitter)
=============================
Earlier I only saw one talk on the new idea Relative Locality, there are now two. They have added one by Laurent Freidel:
http://loops11.iem.csic.es/loops11/index.php?option=com_content&view=article&id=75&Itemid=73
==quote==
The Einstein localisation procedure in relative Locality.
Laurent Freidel
Central Room. Monday, May, 23rd, 17:00 - 17:20.
Abstract:
Relative Locality is a new framework in which the geometry of momentum space is non trivial and spacetime is a derived quantity reconstructed from the momentum space measurement. In order to do so we need to perform the Einstein Localisation procedure which usually allow to reconstruct spacetime from momentum space measurement. We show how this localisation procedure can be performed in Relative locality, how non trivial geometry in momentum space amounts to non locality in spacetime and show explicit physical effects that can be measured in the Gamma ray bursts observations, for instance.
The Principle of Relative Locality.
Lee Smolin
Central Room. Thursday, May, 26th, 10:00 - 10:45.
Abstract:
A new principle is presented which we propose governs the phenomenology of quantum gravity in the regime where the Planck mass cannot be neglected. This involves a deepening of the relativity principle according to which the invariant arena for non-quantum physics is a phase space rather than spacetime. Descriptions of particles propagating and interacting in spacetimes are constructed by observers, but different observers, separated from each other by translations, construct different spacetime projections from the invariant phase space. Nonetheless, all observers agree that interactions are local in the spacetime coordinates constructed by observers local to them. This framework, in which absolute locality is replaced by relative locality, results from deforming momentum space, just as the passage from absolute to relative simultaneity results from deforming the linear addition of velocities. Different aspects of momentum space geometry, such as its curvature, torsion and non-metricity, are reflected in different kinds of deformations of the energy-momentum conservation laws. These are in principle all measurable by appropriate experiments, some of which will be described.
==endquote==
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