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Triangulation Invariant Models from Intertwiner Dynamics

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Bianca Dittrich, Perimeter Institute
08 October 2013 from 10:00 AM to 11:30 AM
320 Whitmore Lab
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Spin foams provide a proposal for a non--perturbative path integral for quantum gravity, based on fundamental building blocks. A key open question to validate this proposal is the continuum limit of the models, which we here understand as the limit including a large number of these building blocks. The complexity of the models made progress difficult.

We will shortly review the program to investigate the problem of the continuum limit first in simpler analogue models.  This helped to develop tools and techniques and most of all approximations and truncations that can be tested on increasingly more complicated models and  in this way to build up  to the full models. 

Here we will introduce a variant of these models which in their algebraic structure (i.e. the structure group) almost reach the full models and are based on the quantum group SU(2)_k. We will construct a procedure to construct triangulation invariant 2D models inside this class of models and argue that these models can be understood as intertwiners implementing simplicity constraints, the key dynamical ingredient of spin foams.

We will discuss the implications for the problem of the continuum limit of spin foams and advertise the triangulation invariant models as new toy theories to test and explore concepts important for background independent systems such as  notions of diffeomorphism symmetry and  Hamiltonian constraints in a discrete.