Description
Book SynopsisThis open access book bridges a gap between introductory Quantum Field Theory (QFT) courses and state-of-the-art research in scattering amplitudes. It covers the path from basic definitions of QFT to amplitudes, which are relevant for processes in the Standard Model of particle physics. The book begins with a concise yet self-contained introduction to QFT, including perturbative quantum gravity. It then presents modern methods for calculating scattering amplitudes, focusing on tree-level amplitudes, loop-level integrands and loop integration techniques. These methods help to reveal intriguing relations between gauge and gravity amplitudes and are of increasing importance for obtaining high-precision predictions for collider experiments, such as those at the Large Hadron Collider, as well as for foundational mathematical physics studies in QFT, including recent applications to gravitational wave physics.These course-tested lecture notes include numerous exercises with solutions. Requiring only minimal knowledge of QFT, they are well-suited for MSc and PhD students as a preparation for research projects in theoretical particle physics. They can be used as a one-semester graduate level course, or as a self-study guide for researchers interested in fundamental aspects of quantum field theory.
Table of Contents1. Introduction & basics
1.1 Poincaré group & representations
1.2. Weyl & Dirac spinors
1.3. Non-abelian gauge theories
1.4. Perturbative quantum gravity
1.5. Feynman-rules
1.6. Spinor helicity formalism for massless particles
1.7. Polarizations
1.8. Color decomposition
1.9. Color ordered amplitudes
1.10. Outlook 1: Massive spinor helicity
1.11. Outlook 2: Momentum twistors
2. Tree-level amplitudes
2.1. BCFW recursion
2.2. 3-point amplitudes
2.3. Factorizations
2.4. Symmetries of scattering amplitudes
2.5. Dualities for gluons & gravitons
2.6. Massive BCFW
2.7. Outlook 1: Scattering eqs. and the CHY Formalism
3. Loop-level integrands and amplitudes
3.1. Introduction
3.2. Unitarity and Cut-Construction
3.3. Generalised Unitarity
3.4. Reduction methods
3.5. General method for one-loop amplitudes
3.5.1. The integral basis
3.5.2. Constructing integrand basis for box, triangle and bubble topologies
3.5.3. D-dimensional integrands and rational terms
3.5.4. Direct construction method (Forde)
3.6. Outlook: multi-loop integrand reduction
4. Loop integration techniques and special functions
4.1. Introduction
4.2. Conventions and Feynman parameter method
4.3. Ultraviolet and infrared divergences
4.4. Mellin-Barnes method
4.5. Feynman integrals and transcedental weights
4.6. Differential equation method
4.7. Functional identities and symbol method
4.8. Other topics
4.9. Exercises
4.10. Outlook, suggested reading for student presentations
5. Exercises with solutions
