Fortgeschrittene Methoden in der Theorie von Streuamplituden
Advanced Topics in the Theory of Scattering Amplitudes

This course provides an introduction to advanced methods used to study multiloop scattering amplitudes in Quantum Field Theory. A rough program will be:

1. Generalised unitarity for one-loop calculations
2. Analytic structure of multiloop Feynman integrals
3. Differential equations for multiloop Feynman integrals
4. General properties of (Chen) iterated integrals
5. Multiple polylogarithms, functional relations and the symbol map
6. Modern ideas on Feynman integrals and general complex hyper-surfaces, the elliptic case

After successful completion of the module the students are able to:

1. Understand generalised unitarity for one-loop scattering amplitudes
2. Understand the analytic properties of multiloop Feynman integrals
3. Use differential equations to evaluate Feyman integrals
4. Understand the basis of the theory of special functions for Scattering Amplitudes

Keine Vorkenntnisse nötig, die über die Zulassungsvoraussetzungen zum Masterstudium hinausgehen.

Blackboard lectures and tutorials

Blackboard lectures, possibly but not necessarily with use of slides to show complicated results

J. Henn and J. Plefka, Scattering Amplitudes in Gauge Theories

R. Ellis, Z. Kunszt, K. Melnikov, G. Zanderighi, One-loop calculations in quantum field theory: from Feynman diagrams to unitarity cuts https://arxiv.org/pdf/1105.4319.pdf

C. Duhr, Mathematical Aspects of Scattering Amplitudes https://arxiv.org/pdf/1411.7538.pdf

T. Gehrmann, E. Remiddi, Differential Equations for two-loop four point functions https://arxiv.org/pdf/hep-ph/9912329.pdf

M. Argeri, P. Mastrolia, Feynman Diagrams and Differential Equations https://arxiv.org/pdf/0707.4037.pdf 

There will be an oral exam of 25 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using comprehension questions and sample calculations.

For example an assignment in the exam might be:

• Describe the properties of polylogarithms
• Derive and solve differential equations for a simple integral
• Use generalised unitarity to compute a simple amplitude

Participation in the exercise classes is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.