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Modern Methods of Quantum Chromodynamics (WS14/15)


PD Dr. Christian Schwinn


  • Lecture: 3 hours, Wed 12-14, SR 2.OG Westbau, Fr 14-15 SR GMH
  • Tutorial: 1 hour, Fr 15-16,  SR GMH

The lecture is suitable as an elective course  (7 Credit points) in the master progam.  


Quantum Chromodynamics (QCD) is the theory of interactions of quarks and gluons, the constituents of the proton and other hadrons. The ability to make precise predictions in QCD is therefore essential for the understanding of physics at the Large Hadron Collider. In the last 10 years, there have been tremendous advances in the understanding of scattering amplitudes in QCD and new methods for the construction of amplitudes with a large number of external particles have been developed, partly based on insights from Supersymmetry, string theory or twistor theory. This lecture will give a basic introduction to QCD  and the application of these modern methods to the calculation of scattering amplitudes. 


  • Parton model, QCD Lagrangian, Feynman rules
  • Properties and construction of multi-leg tree amplitudes (Spinor helicity methods, Schwinger-Dyson equations, Colour decomposition, recursive constructions)
  • Overview of loop calculations in QCD (One-loop calculations, Renormalization group, factorization)
  • Introduction to unitarity methods for loop calculations (Cutkosky rules, modern unitarity and on-shell methods)


Advanced Quantum Mechanics, desirable: Introduction to Relativistic Quantum Field Theory.

Lecture notes

Lecture notes will be made available during the lecture: (pdf file) (version of 30.03. 2015)


  • M. Schwartz, "Quantum field theory and the standard model", Cambridge University Press (2014)
  • M. Mangano, "Introduction to QCD" (1998), pdf file.
  • G. Dissertori; I. Knowles; M. Schmelling, "Quantum chromodynamics : high energy experiments and theory ", Oxford University Press (2003)
  • M. Peskin, "Simplifying Multi-Jet QCD Computations", arXiv:1101.2414 [hep-ph]
  • L. Dixon, "A brief introduction to modern amplitude methods", arXiv:1310.5353 [hep-ph] 

More advanced literature

  • J. Henn,  J. Plefka, "Scattering amplitudes in gauge theories" (Lecture notes in physics; 883), Springer (2014)
  • K. Ellis et al.  "One-loop calculations in quantum field theory: from Feynman diagrams to unitarity cuts", arXiv:1105.4319 [hep-ph] 

Some original papers

  • R. Britto, F. Cachazo, B. Feng, E. Witten, "Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory", arxiv:hep-th/0501052

Background in Quantum Field Theory

  • S.Dittmaier, H. Rzehak, C. Schwinn, "Introduction to Relativistic Quantum Field Theory", lecture notes (pdf file)
  • M.Maggiore, "A Modern Introduction to Quantum Field Theory"
  • Weinberg: "The Quantum Theory of Fields, Vol.1: Foundations"

Requirements for Academic Record

  • active and regular participation in the tutorials, including solutions to  50% of the homework problems.

Further details will be given in the lecture/tutorials.

  1. Problem set (pdf file)
  2. Problem set (pdf file
  3. Problem set (pdf file
  4. Problem set (pdf file)
  5. Problem set (pdf file
  6. Problem set (pdf file) (for tutorial on 30.01)
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