Recently Jorma Louko, Steven Kerr and I produced a state sum model with fermionic variables. It is only in 1d space-time, so something of a toy model, but it illustrates some important principles. Firstly, the model is triangulation-independent, which means it has the “diffeomorphism symmetry” of general relativity. Secondly, the fermion integration induces an action for the bosonic gauge field (as expected) but without a cosmological constant (very unexpected). I’m still somewhat puzzled over exactly how that works, but it would be very nice if there are models like that in higher dimensions.
The lecture slides are available on the page Talks: slides and videos.
My father died last summer – hence the big gap in posts while I catch up with everything else. There’s lots of things I could say about him – his love of games and puzzles for example. But here I just want to explain one thing: he taught me my first mathematics at the age of nine or ten, some trigonometry and algebra. I can remember finding mathematics at school easy and I am sure that what he taught me helped greatly. It wasn’t so much knowing the trigonometry and algebra that was so helpful, more that I understood from him how to go about doing mathematics. That seems to me to be a very important part of teaching.
Here at Nottingham we are running an MSc in Gravity, Particles and Fields. This is very specifically aimed at students interested in getting into relativity and particle physics research, in areas such as quantum gravity, cosmology, quantum information, etc.
The MSc runs from each September and applications can be made online at any time. More info
Update There are some grants for well-qualified students, the details depending which country you are from (or currently in). Details are under the funding tab.
I gave a short talk at IHES in December (and a rather longer one in Marseille, too) on the topic of modifying quantum gravity models so that they contain realistic matter. A lot of work on quantum gravity is done without any matter fields and one gets the impression that matter fields are an optional extra which just make the system more complicated. The icing on the cake, as Chris Isham used to say about topology.
In my talk I suggested that, on the contrary, quantum gravity models with matter can actually be rather simpler than models without matter. This is because the Einstein action is induced by the matter fields, so removing the requirement to put the Einstein action into the theory from the beginning.
Some slides from my talks at Bayrischzell and Oxford are available. I am writing a short paper expanding this.
Update (Feb ’11) The paper is out now. The key observation is that the bosonic part of the gravity+standard model action can be obtained from a functional integral over fermions. It seems a strange idea that physics is really like this, but then how else to account for such a wonderful accident?
[Note: The paper is somewhat preliminary and I hope to get back to it and add some more detail in a revised version later.]