Scattering Amplitudes in Quantum Field Theory
Scattering amplitudes play a crucial role in Quantum Field Theory (QFT) by providing a method to extract phenomenological predictions for particle scattering. They are on-shell, gauge-invariant objects that do not suffer from the ambiguities inherent to off-shell expansions in Feynman diagrams. The cross-section for a given process can be computed by integrating the scattering amplitude squared on the phase-space of the produced particles. These amplitudes exhibit unexpected symmetries and a simplified structure compared to the Lagrangian formulation of QFT.
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Modern methods for calculating scattering amplitudes focus on tree-level amplitudes, loop-level integrands, and loop-integration techniques. These methods reveal intriguing relations between gauge and gravity amplitudes and are of increasing importance for collider experiments and foundational mathematical physics studies in QFT.
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The state of the art in amplitude computation has advanced significantly, with modern approaches using gauge-invariant building blocks to organize calculations. Perturbative unitarity has allowed the writing down of relations that recycle these gauge-invariant building blocks, leading to a recursion in the number of particles and the loop order. This has led to a deeper understanding of the analytic structure of scattering amplitudes in gauge theory and gravity.
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For those interested in the mathematical and theoretical aspects of scattering amplitudes, lecture notes and textbooks are available that cover the path from basic definitions of QFT to amplitudes relevant for processes in the Standard Model of particle physics. These resources are suitable for MSc and PhD students as preparation for research projects in theoretical particle physics
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