Scattering Amplitudes in Quantum Field Theory

ISBN-13: 9783031469862 / Angielski

Simon Badger; Johannes Henn; Jan Christoph Plefka

Spis treści

1.     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

O autorze

Prof. Simon Badger received his doctorate in theoretical physics in 2006 from Durham University in the UK. He has held a number of research appointments including the Niels Bohr Institute, CERN, the University of Edinburgh and Durham University. He joined the University of Turin as associate professor in 2020. He works on multi-loop scattering amplitudes in the Standard Model and precision LHC phenomenology. He was awarded a Consolidator Grant from the European Research Council for the project "High precision multi-jet dynamics at the LHC" in 2018.

Prof. Dr. Johannes Henn received his doctorate in physics from Lyon University in 2008, and has held research appointments at Humboldt University Berlin, the Institute for Advanced Study Princeton, and Mainz University. In 2018, he was appointed to the Max Planck Institute for Physics as a Director. He works on mathematical structures in quantum field theory, with a focus on applications to multi-loop scattering amplitudes. In 2017, he received a Consolidator Grant from the European Research Council with the project "Novel structures in scattering amplitudes".

Prof. Dr. Jan Plefka studied physics at the TU Darmstadt and Texas A&M University receiving his doctorate in theoretical physics from Hannover University in 1995. He held research appointments at City University New York, NIKHEF Amsterdam and the Max-Planck Institute for Gravitational Physics in Potsdam. In 2006 he was appointed as associate and 2011 as full professor for theoretical physics at Humboldt-Universität zu Berlin. He works on aspects of quantum field theory and gravity, with a focus on scattering amplitudes, gauge-gravity dualities, hidden symmetries and applications of amplitude techniques to classical gravitational wave physics. He received an Advanced Grant from the European Research Council with the project "High-Precision Gravitational Wave Physics from a Worldline Quantum Field Theory" in 2023.

Dr. Simone Zoia received his doctorate in physics from Ludwig Maximilians University Munich in 2021, after carrying out research at Mainz University and at the Max Planck Institute for Physics. Currently, he holds a post-doctoral position at the University of Turin. He works on multi-loop scattering amplitudes and Feynman integrals, with a particular interest in their mathematical properties and in analytic techniques. In 2023, he was awarded a Marie Skłodowska-Curie fellowship from the European Research Council.

Blurb

This 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.