The Algebra & Geometry of Modern Physics

Loop Quantum Gravity (LQG) aims at a manifestly background independent quantization of General Relativity. The basic building block of the so-called spin-foam models, a covariant version of LQG, is the 4-simplex amplitude that gives rise to a discrete quantum geometry. I will derive this 4-simplex amplitude and analyse its semi-classical properties using spinor techniques. In order to do so we will have to introduce SU(2)-coherent states in the sense of Perelomov which are closely connected to the geometric interpretation of spinors.