PhD project: General properties of gauge-theory scattering amplitudes

Project description

Our understanding of the fundamental interactions is largely based on collider experiments where particles are scattered at high energy. The theoretical description of these processes is based on scattering amplitudes, which are computed in quantum field theory as a perturbative expansion in the coupling. Amplitudes in gauge theories also have an intriguing mathematical structure relating directly to deeps aspects of the underlying dynamics, such as the fact that the interactions are local, and that the total probability for producing any state in a scattering experiment sums to unity. We are studying general properties of scattering amplitudes from several different perspectives (which sometimes overlap): 

  1. Long-distance singularities: it is well known that gauge theory amplitudes has long-distance singularities. We are studying the detailed structure of these singularities for multi-leg processes in general kinematics, where we are able to gain rather detailed information on quantum corrections at the multi-loop level.
  2. Special kinematic limits: upon considering amplitudes in special kinematic limits, such as the high-energy limit (the limit where the centre of mass energy is much larger than the momentum transfer) or collinear limits where the momenta of two or more particles coincide, the amplitudes significantly simplify and can be investigated to high loop order, and sometimes to all orders in perturbation theory. 
  3. The analytic structure of amplitudes. Feynman integrals are analytic functions of the kinematic variables, and their singularities (poles and cuts) relate to their physical properties. Recent progress in understanding the class of functions needed to express the results of such integrals (e.g. generalised polylogarithms) allows us to develop better techniques to compute them and also also to develop a more complete picture of the relation between the underlying mathematical structure and physics.

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