Modern approaches to scattering amplitudes – University of Copenhagen

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Modern approaches to scattering amplitudes

Recent years have seen tremendous advances in both our understanding of quantum field theory and in our ability to make predictions for experiment. The predicted probabilities for all the possible outcomes of any experiment are encoded by functions called scattering amplitudes. These are the bread and butter of quantum field theory. 

Although the traditional formalism of Feynman diagrams provides an intuitive and ultimately correct way to compute scattering amplitudes, they require vast computational resources to make even simple the simplest amplitudes and obscure a deep (and near universal) simplicity and beauty ultimately discovered for the mathematical form of the predictions made. So long as we find this simplicity surprising, it cannot be said that we truly understand quantum field theory.

This situation has changed dramatically in recent years. A number of powerful new mathematical and computational techniques have been discovered and developed that dramatically improve our understanding of the simplicity of amplitudes and our ability to compute them. These revolutionary new tools include recursion relations, twistor string theory (and string theory more generally), the Q-cut formalism, generalized unitarity, the scattering equation formalism, and a surprising connection between scattering amplitudes and the geometry of Grassmannian manifolds. All of these approaches are being studied and developed by researchers at the NBIA which hosts the world’s largest concentration of expertise in these exciting developments.

Examples of the research being pioneered by researchers at the NBIA
include:

  • Exploring the connection between scattering amplitudes in
    four-dimensional theories and Grassmannian geometry.
  • Developing powerful reformulations of perturbation theory; these include: extending on-shell recursion relations to (more) general theories,
    extending the scattering equation formalism to more theories and to higher orders, and enhancing unitarity-based methods to the integrand-level.
  • The discovery of a new “Q-cut” representation of scattering amplitudes
    in perturbation theory that is free of the redundancies of the Feynman
    expansion.
  • Studies of perturbative quantum gravity in effective field theory and
    its consequences for the scattering of lightlike matter around the sun.
  • Improving our understanding of (and our ability to compute) the
    transcendental functions relevant to scattering amplitudes in perturbation theory.