Scattering Amplitudes in Quantum Field Theory

This course provides an introduction to modern methods in perturbative Quantum Field Theory, which find their primary application in high-energy physics

- Representations of the Lorentz and Poincare group, little group and spinor representations

- Spinor helicity formalism for Scattering Amplitudes

- Tree-Level amplitudes, color decomposition and primitive amplitudes, recursion techniques

- Loop amplitudes and treatment of UV and IR divergences in dimensional regularization

- Optical theorem, dispersion relations and the analytic structure of scattering amplitudes

- Basics of Generalized unitarity for one-loop scattering amplitudes

- Introduction to Modern multiloop techniques (Direct Integration techniques, Integration by Parts identities, Differential Equations)

- Introduction to the theory of Special Functions (classical polylogarithms, multiple polylogarithms and the symbol map, generalizations)

After successful completion of the module the students understand modern ideas and methods in the theory of Scattering Amplitudes in perturbative Quantum Field Theory. In particular, the students:

1. Can use the spinor helicity formalism and recursive methods for tree-level amplitudes in Yang-Mills theories.
2. Understand the origin of IR and UV divergences in scattering amplitudes
3. Can decompose scattering amplitudes in independent master integrals and understand their analytic properties
4. Know how to compute one-loop Feynman integrals in dimensional regularization by direct integration
5. Can apply integration by parts identities and differential equations to Feynman integrals
6. Have an understanding of the basic properties of iterated integrals and in particular of polylogarithms

Very good knowledge of Advanced Quantum Mechanics and Special Relativity are essential.

A knowledge of Quantum Field Theory as provided in PH2040 (Relativity, Particles and Fields) and PH1008 (Quantum Field Theory) would be desirable. In particular, familiarity with Scalar, QED and Yang Mills Feynman rules will be assumed for some parts of the course.

Very motivated students can profit from this class by attending it in parallel with PH1008.

Blackboard lectures and weekly exercises

Blackboard lectures, possibly (but not necessarily) accompanied by slides

- Quantum Field Theory and the Standard Model, M. Schwartz

- Scattering Amplitudes in Gauge Theory and Gravity, H. Elvang and Y.T. Huang

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

- Calculating Scattering Amplitudes Efficiently, L. Dixon https://arxiv.org/abs/hep-ph/9601359

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: Computation of Tree Level amplitudes with Recursion Techniques; Discussion of Properties of One Loop Feynman Integrals;

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