# 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.