Scientific curriculum

Scientific curriculum

Training in the following scientific areas will be provided at the SAGEX schools. Please see the event listings for further details.


  • Quantum Field Theory including Feynman diagrams and traditional perturbative methods.

Basics of Amplitudes

  • Kinematics and building blocks (color decomposition, spinor helicity formalism, twistor variables, momentum twistors).
  • Tree-level technology, in particular recursions (off-shell currents (Berends-Giele), onshell (BCFW), CSW rules).

Loop-Level Technologies

  • Amplitude decompositions (Master Integrals, IBP, Laporta algorithm).
  • Computation of integral coefficients (unitarity, generalised unitarity, D-dimensional methods, OPP algorithm).
  • Integration and summation strategies (Feynman and Mellin-Barnes representations, differential and difference equations, symbolic summation and integration).
  • Mathematical structure of loop amplitudes (generalized polylogarithms, symbols, Hopf algebra structure, iterative and non-iterative sums).
  • Computer algebra tools (FORM, Mathematica, FeynArts, FormCalc).

Specialised topics in Amplitudes

  • Factorisation properties of amplitudes (soft/collinear).
  • IR cancellation between real and virtual contributions.
  • Landau singularities and Landau equations.
  • Regge Kinematics.
  • Collider physics (extracting predictions from amplitude calculations).
  • Twistor actions.
  • Basics of Grassmannian geometry.
  • Near-collinear kinematics and the Pentagon Operator Product Expansion.


  • Super(conformal)symmetry (on shell superspace/superamplitudes, SUSY Ward identities, SUSY BCFW recursion).
  • Hidden symmetries and integrability (Dual conformal symmetry, Yangians, 2d S-matrices, N=4 SYM, ABJM).
  • Asymptotic symmetries and soft theorems.

String Theory and String-inspired methods

  • Basics of string amplitude computation (open and closed strings).
  • KLT in string theory and field theory.
  • Color-kinematics duality and double copy.
  • CHY formulae.
  • AdS/CFT correspondence.