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- Sebastian Steinhaus

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In my research on quantum gravity, I mainly focus on discrete approaches, e.g. spin foam model, which is a path integral approach closely related to loop quantum gravity. A typical spin foam can be imagined to mediate between an initial and final 3D geometry, which are given by spin network states. Then the spin foam assigns an amplitude to this transition by summing over all 4D geometries compatible with this boundary data.

In any discrete theory, we must address the question whether the dynamics are consistent, that is do not depend on the ambigious choices made in its definition, and how to establish a connection back to well-known continuum physics. Indeed, both issues are crucial for making contact with observations eventually.

Both these issues can be tackled by studying renormalization of spin foams; the idea is the following: consider a coarse and a fine boundary. The fine boundary can naturally store more information, i.e. it comes with a larger Hilbert space, but, given a coarse state, this state can also be represented in the finer, more complex, Hilbert space. Relating and identifying states across Hilbert spaces is crucial, since we can then compare coarser and finer spin foams for the *same* transition. Generically we have to assign different spin foam amplitudes to both discretisations to get consistent results giving a renormalization group flow of amplitudes.

To implement such a procedure using numerical methods is indispensable. A very useful tool is tensor network renormalization, another research focus at Perimeter. Recently I have also studied simplified, restricted 4D spin foam models using Monte Carlo methods and found encouraging results, e.g. indications for a UV-attractive fixed point. In addition to extending on these previous results, I am also looking at extracting effective quantities out of spin foams, e.g. their spectral dimension, and coupling matter to the dynamical geometry encoded in a spin foam.

- Renormalization in symmetry restricted spin foam models with curvature, Benjamin Bahr, Giovanni Rabuffo and Sebastian Steinhaus, arXiv: 1804.00023
- Emergence of Spacetime in a restricted Spin-foam model, Sebastian Steinhaus and Johannes Thürigen, arXiv: 1803.10289

©2012 Institut Périmètre de Physique Théorique