P23.1.2a Scattering amplitudes in gauge theories
Prof. Dr. Jan Plefka, Summerterm 13 Lectures: Thu 15-11 NEW 15 2’102 and Wed 13-15 NEW 15 2’101 Problem sessions: Wed 13-15 NEW 15 2’101
On Wednesdays the lecture and problem sessions will alternate weekly see precise dates below.
Topics
I. Introduction and Basics
(Motivation; Lorentz-group & representations; Weyl & Dirac spinors, Lagrangians ; Yang- Mills theory & Feynman rules)
II. Tree-Level Amplitudes
(Color decomposition; spinor helicity formalism; analytic properties (soft & colinear li- mits); Helicity classification of gluon amplitudes (Parke-Taylor); BCFW recursion rela- tions, Poincar´e and conformal symmetry; Massive particles, ∗Higher dimensions, N = 4 super Yang-Mills on-shell superspace and superamplitudes, ∗Grassmannian approach to N = 4 super amplitudes)
III. Loop-Level Structure
(Integral reduction at one-loop, generalized unitarity method, techniques for the eva- luation of loop integrals (integration by parts, dual conformal symmetry, Mellin-Barnes representations, differential equations)
IV. Symmetries & Dualities
(Wilson loop/scattering amplitude duality; Dual conformal symmetry; Yangian/Dual su- perconformal symmetry at tree-level)
V. Outlook
5 SWS, 5 SP/ECTS, Oral exam for the completion of module P23.1.2a possible.
Dates:
Lectures: 10.4, 11.4, 18.4, 24.4, 25.4, 8.5, 16.5, 22.5, 23.5, 30.5, 5.6, 6.6, 13.6, 19.6, 20.6, 27.6, 3.7, 4.7, 11.7
Problem sessions: 17.4, 2.5 (irregular), 15.5, 29.5, 12.6, 26.6, 10.7
Literature:
A hardcopy of lecture notes authored by J.M Henn and J. Plefka will be handed out in class.
Furthermore the following references are recommend:
• L. J. Dixon. Calculating scattering amplitudes efficiently. TASI lectures, hep-ph/9601359
• Ellis, Kunszt, Melnikov, Zanderighi. One-loop calculations in QFT: From Feynman dia- grams 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. cattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence. Phys. Rept. 468, 153-211 (2008). [arXiv:0807.1889 [hep-th]]
• J.M. Henn. Duality between Wilson loops and gluon amplitudes. Fortsch. Phys. 57, 729- 822 (2009). [arXiv:0903.0522 [hep-th]]
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