ITP Lecture Archive

**Lecturer:** Prof. Jan Plefka

Tuesday 9:45-11:30, HIT F 32

**Assistant:** Matteo Rosso

Wednesday 13:45-14:30, HIT H 51

**Biweekly Schedule in February and March:**

Tuesday: 18.02./04.03./18.03.: 9:45-11:30 (lecture)

Tuesday: 18.02./04.03./18.03.: 13:45-15:30 (lecture)

Wednesday: 26.02./12.03./26.03.: 12:45-14:30 (exercises)

This advanced course will introduce students into modern methods for the efficient calculation of scattering amplitudes in gauge theories. In recent years so-called on-shell methods based on generalized unitarity have been established, which have been proven to be more efficient than the traditional Feynman graph based method of calculating scattering amplitudes. The lecture will discuss tree-level and one-loop amplitudes in massless gauge theories without and with maximal supersymmetry.

Prerequistes are quantum field theory I and a basic knowledege of the standard model of particle physics, ideally also quantum field theory II which should at least be taken in parallel.

- Introduction and Basics (Motivation; Lorentz-group & representations; Weyl & Dirac spinors, Lagrangians; Yang-Mills theory & Feynman rules)
- Tree-Level Amplitudes (Color decomposition; spinor helicity formalism; analytic properties (soft & colinear limits); Helicity classification of gluon amplitudes (Parke-Taylor); BCFW recursion relations, Poincaré and conformal symmetry; Massive particles, N = 4 super Yang-Mills on-shell superspace and superamplitudes)
- Loop-Level Structure (Integral reduction at one-loop, generalized unitarity method, techniques for the evaluation of loop integrals (integration by parts, dual conformal symmetry, Mellin-Barnes representations, differential equations)
- Symmetries & Dualities (Onshell recursion at loop level, Wilson loop/scattering amplitude duality; Dual conformal symmetry; Yangian/Dual superconformal symmetry at tree-level)

- Johannes M. Henn, Jan C. Plefka. Scattering Amplitudes in Gauge Theories, Lecture Notes in Physics 883 (2014), Springer
- L. J. Dixon. Calculating scattering amplitudes efficiently. TASI lectures, hep-ph/9601359
- Ellis, Kunszt, Melnikov, Zanderighi. One-loop calculations in QFT: From Feynman diagrams to unitarity cuts. Physics Reports 518 (2012) 141-250; arXiv:1105.4319
- J. Drummond. Hidden simplicity of gauge theory amplitudes. arXiv:1010.2418
- M. Srednicki. Quantum field theory. Cambridge University Press
- L.F. Alday, R. Roiban. Scattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence. Phys. Rept. 468, 153-211 (2008). arXiv:0807.1889
- J.M. Henn. Duality between Wilson loops and gluon amplitudes. Fortsch. Phys. 57, 729- 822 (2009). arXiv:0903.0522

- 20 minute oral examination
- Recommended: 70% of homework problems worked out in reasonable quality
- Recommended: 1 problem solution presented at black board