overview of research

The following overview contains technical terms. I hope to add a non-technical summary soon!

Spacetime represents one of the remaining frontiers in theoretical physics. We have successful theories of fields in spacetime and of the geometry of spacetime. But there is no established theory of spacetime itself, a theory that would explain why we live in a spacetime and not in something
completely different.

My research contributes to attempts to find such a theory. So far I have mostly worked on loop quantum gravity and spin foam models, but I am also open to various other approaches such as noncommutative geometry, causal sets, quantum graphity and matrix models. All these research directions have in common that they aim to explain spacetime manifolds in terms of more fundamental objects. They try to produce space from no space.

Loop quantum gravity and spin foam models are theories whose quanta (or particles) are given by elementary cells of spacetime such as triangles and tetrahedra. It is hoped that spacetime as a whole arises through the interaction of many of these quanta. Whether this is indeed the case is an open question and often referred to as the problem of the semiclassical limit.

In joint work with Laurent Freidel, I have investigated this semiclassical limit and shown that spin foam models reduce to a certain form of Regge calculus, another formulation of quantum spacetime. This reduction is an important consistency check; if it failed, the theory would not have the degrees of freedom of gravity.

Another of my projects concerned the signature and causal structure in spin foam models. Previously spin foam models were exclusively defined with spacelike triangles, and it was not known how to implement timelike triangles. This is a problem, since it means that all edges of discrete spacetime are spacelike and it is not clear how to couple matter particles to
it (which have timelike worldlines). In work together with the Master's student Jeff Hnybida, I have shown how the inclusion of timelike triangles can be achieved and an associated extended model of spin foams was defined. Remarkably, the area of timelike surfaces is quantized in a similar way as for spacelike surfaces.

Recently I finished work on a model of quantum graphity that gives a successful example of the 'space from no space' idea. It is a statistical model of graphs in which 2-dimensional spaces arise as ground states. An intuitive explanation of the model is given here, together with videos of simulations.