Maths HEP Lunchtime Seminars: Conformal invariance in momentum space
2 December 2016 13:00 in CM221
Conformal invariance places powerful constraints on the observables of a quantum field theory. In position space, 2- and 3-point correlators at separated points take a well known form that is completely determined by this symmetry. In this talk, we construct the corresponding story in momentum space. Starting from first principles, we determine the momentum-space 2- and 3-point functions of a general conformal field theory. For certain spacetime and operator dimensions, a non-trivial renormalisation is required reflecting the presence of contact terms when operator insertions coincide. We show how to perform this renormalisation directly in momentum space leading to novel conformal anomalies and beta functions. We also discuss the form of correlators with tensor structure including stress tensors and conserved currents. The results have potential applications to many fields including holographic cosmology and condensed matter physics.