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Advanced Topics in the Theory of Scattering Amplitudes

Module PH2320

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Basic Information

PH2320 is a semester module in English language at Master’s level which is offered in winter semester.

This Module is included in the following catalogues within the study programs in physics.

  • Specific catalogue of special courses for nuclear, particle, and astrophysics
  • Complementary catalogue of special courses for condensed matter physics
  • Complementary catalogue of special courses for Biophysics
  • Complementary catalogue of special courses for Applied and Engineering Physics
  • Specialization Modules in Elite-Master Program Theoretical and Mathematical Physics (TMP)

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workloadContact hoursCredits (ECTS)
150 h 60 h 5 CP

Responsible coordinator of the module PH2320 is Lorenzo Tancredi.

Content, Learning Outcome and Preconditions


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

Learning Outcome

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


A knowledge of Quantum Field Theory, including on-shell methods will be assumed, in particular the spinor helicity formalism and recursion relations at tree level.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VO 2 Advanced Topics in the Theory of Scattering Amplitudes Tancredi, L. Thu, 08:00–10:00, PH 3344
UE 1 Exercise to Advanced Topics in the Theory of Scattering Amplitudes
Responsible/Coordination: Tancredi, L.
dates in groups

Learning and Teaching Methods

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

C. Duhr, Mathematical Aspects of Scattering Amplitudes

T. Gehrmann, E. Remiddi, Differential Equations for two-loop four point functions

M. Argeri, P. Mastrolia, Feynman Diagrams and Differential Equations 

Module Exam

Description of exams and course work

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.

Exam Repetition

The exam may be repeated at the end of the semester.

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