Paul Bird's Scientific Research

Why should N=8 Supergravity be finite? I would like to attempt to explain here why adding N=8 supersymmetry to General Relativity should have the chance of making the theory finite. Firstly, it is known that the only renormalizable theories are those of spin 0, spin 1/2 and spin 1 particles.  General Relativity, however, is quantized by spin 2 particles - gravitons . (Adding simple N=1 supersymmetry to GR also adds spin 3/2 particles - gravitinos ). If we add N=8 supersymmetry we have a single super-particle whose components compose of spin 2, 3/2, 1, 1/2, 0 , -1/2, -3/2, -2 particles. We can think of this as some kind of super-vector. There are (1,8,28,56,72,56,28,8,1) of each of these types of particles respectively. What we would like to do is get rid of these spin 2 and spin 3/2 components (18 of them) because they are non-renormalizable. So, we should like to be able to rotate this super-vector in such a way that these components become zero. We also, need to rotate this s

Three-point Green's function in position space In this post I'm trying to calculate the 3-point interaction function for quantum field theory in position space. It sounds simple enough. It is just calculating the 4 dimensional integral over w of:   Δ(x-w) Δ(y-w) Δ(z-w)   which should produce a symmetric function in three variables: A(|x-y|,|y-z|,|z-x|) however it turns out to be extremely complicated to get a nice formula in terms of symmetric variables. See here for my notes on it so far It would be nice to relate this function to geometric properties such as the area of the triangle but that doesn't seem to be the case. Only the sums of the powers of the lengths of the sides which are symmetric forms. I have a series solution for the case when m is not zero but can't find a solution for when m=0. If anyone can help let me know!

Concise Rules of the Universe In this post I was taking the challenge of instilling all the rules of the Universe that we know of into one side of A4. More technically: taking an embedding of the Standard Model into the low energy sector of a Superstring Theory and try to give all the rules for this as concisely as possible. It is a useful exercise because, as people say, if you can't explain something simply, you probably don't really understand it yourself. It turns out that it is not so simple to do. Particularly describing the particle content of N=8 Supergravity is trivial but stating which interactions are allowed is more complicated. Unless someone knows a simple description? Concise Rules of the Universe Have a go yourself!

The Feynman Diagrams for the Big Bang It is sometimes said that the moment of the Big Bang is beyond the scope of science. I disagree with that statement. If the Big Bang is within the realms of Quantum Field Theory then we should be able to draw Feynman diagrams starting from the Big Bang singularity. These Feynman diagrams are very special because they necessarily have an infinite world number of lines drawn out of the point T=0. However, it turns out that when transforming the description to cosmological time, this simply means that an infinite number of particles are created at the Big Bang forming a Poisson distribution. The most likely candidate for the identity of these infinite number of particles are gravitons, as there is no limit to the number of gravitons that can be emitted in a single interaction. The other alternative is that we must simply sum over every possible configuration of particles. The full paper is here: Feynman Diagrams of the Big Bang  (aka Modelli

Einstein Field Equations in Polynomial Form Einstein's Field equations (and the action from which it is derived) are sometimes, I would say mistakenly, said to be `highly non-polynomial'. This little article explains one method of writing the equations so they are polynomial in a redefinition of the metric tensor to a suitable metric tensor-density .  Einstein's Gravitational Field Equations in Polynomial Form Another way to put the equations in polynomial form when there is a diliton field such as in Brans-Dicke gravity is to absorb the determinants of the metric into the definition of the diliton field.