Abstract:

We introduce Fermionic quantum cellular automata and describe the emergence of different geometries from their structure, under the assumptions of linearity, unitarity, locality, homogeneity and isotropy. We show how homogeneity gives rise to a translation group structure through the construction of a Cayley graph. In the Abelian case the large-scale automaton dynamics can be described by the equations of free relativistic Weyl quantum fields. We provide a non-linear Lorentz symmetry for the emergent space-time in this case. We then review the main problems in the non-Abelian case, showing a renormalization technique for the virtually Abelian case.

Short Bio: