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Scattering Amplitudes in Quantum Field Theory
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Scattering Amplitudes in Quantum Field Theory
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These lecture notes bridge a gap between introductory quantum field theory (QFT) courses and state-of-the-art research in scattering amplitudes. They cover the path from basic definitions of QFT to amplitudes relevant for processes in the Standard Model of particle physics. The book begins with a concise yet self-contained introduction into 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 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 CERN's 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 detailed 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 QFT. Supplementary material, Mathematica notebooks, corrections and further information are provided and maintained at the dedicated website https://scattering-amplitudes.mpp.mpg.de/scattering-amplitudes-in-qft/ .
Forward citations
Cited by 9 Pith papers
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Bootstrapping two-loop six-gluon amplitudes in QCD
A symbol bootstrap using leading singularities determines the maximal-weight symbol of the planar two-loop six-gluon amplitude in massless QCD for MHV configurations.
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Resonance and Differential Reduction of Feynman Integrals
The paper develops reduction operators from resonance in GKZ systems to contract edges in Feynman graphs for one-loop, sunrise, and banana graphs, closing differential equation systems to master integrals.
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Fine-Tuning Small Reasoning Models for Quantum Field Theory
Small 7B reasoning models were fine-tuned on synthetic and curated QFT problems using RL and SFT, yielding performance gains, error analysis, and public release of data and traces.
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Negative running of gravitational positivity
Non-minimal three-point interactions induce negative one-loop running of Wilson coefficients in gravitational EFTs, yet graviton loops generate positive IR contributions that dominate the bounds after smearing if the ...
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QCD Scattering Amplitudes and Prescriptive Unitarity
The maximally-transcendental part of planar two-loop six-gluon MHV QCD amplitudes is bootstrapped at symbol level and expressed in a 137-letter alphabet.
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Two-loop all-plus helicity amplitudes for self-dual Higgs boson with gluons via unitarity cut constraints
Two-loop all-plus helicity amplitudes for self-dual Higgs plus gluons are obtained via four-dimensional unitarity cuts into one-loop and tree amplitudes plus finite-field tensor reduction.
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Massive On-shell Splitting Functions in Spinor-Helicity Formalism
Massive SM splitting functions are reconstructed from on-shell amplitudes via SW collinear spinors and a Higgs-insertion dictionary.
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Operator Product Expansion in Carrollian CFT
Constructs Carrollian OPEs that govern short-distance behavior, extends representation theory for composites, and classifies 2-, 3-, and 4-point correlators/amplitudes under Carrollian symmetry.
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Graphical Functions by Examples
Graphical functions, defined as massless three-point position-space integrals, serve as a powerful tool for evaluating multi-loop Feynman integrals, with extensions to conformal field theory and recent algorithmic com...
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