Abstract
Scattering amplitudes in quantum field theories are of widespread interest, due to a large number of theoretical and phenomenological applications. Much is known about the possible behaviour of amplitudes, that is independent of the details of the underlying theory. This knowledge is often neglected in modern QFT courses, and the aim of these notes - aimed at graduate students - is to redress this. We review the possible singularities that amplitudes can have, before examining the generic behaviour that can arise in the high-energy limit. Finally, we illustrate the results using examples from QCD and gravity.
Highlights
Can we find common languages, that make e.g. QCD and gravity look the same? Even though the physics in different theories can vary greatly, it might be possible to interpret this physics through a common calculational procedure, that itself makes clear why the physical behaviour is forced to be different
The Regge limit is relevant for the scattering of black holes, or other high energy objects. This is of interest due to the recent discovery of gravitational waves by LIGO, and for studies which aim to explore the possible existence and structure of a gravitational S-matrix if we go above the Planck scale
We look at the Regge limit, and deduce that amplitudes must generically grow in a power-like way as the energy becomes large, where this growth can be associated with the exchange of an infinite family of bound states. We illustrate this with examples in QCD and gravity. The behaviour in those two theories will be very different, the calculations themselves will be very similar, and both agree with the generic predictions that come from S-matrix theory
Summary
Much research in contemporary theoretical high energy physics involves scattering amplitudes (see e.g. refs. [1, 2] for recent reviews), which are themselves related to the probabilities for interactions between various objects to occur. The Regge limit is relevant for the scattering of black holes, or other high energy objects This is of interest due to the recent discovery of gravitational waves by LIGO, and for studies which aim to explore the possible existence and structure of a gravitational S-matrix if we go above the Planck scale One can show that at high energy, amplitudes have similar overall behaviour, regardless of the underlying theory This allows us to interpret modern results, clarify their structure, and provides important crosschecks for new calculations. The behaviour in those two theories will be very different, the calculations themselves will be very similar, and both agree with the generic predictions that come from S-matrix theory
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