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Scattering Amplitudes + Dualities at Infinity: Part 1
Learn how modern physicists rethink scattering amplitudes by moving away from spacetime Feynman diagrams and exploring the geometry of kinematic space.
Lecture guide · Written by AI from the lecture. For the lecture’s own words, open the Transcript tab.
Explores scattering amplitudes in flat space as boundary observables, contrasting traditional spacetime trajectory stories with modern geometric and holographic formulations. Focusing on a toy model of trace phi-cubed theory, the discussion introduces kinematic space coordinates like X_ij variables, momentum polygons, and their connections to Catalan numbers, Feynman diagram triangulations, and string-theoretic moduli spaces.
This lecture assumes
- Quantum Mechanicstaught in The Future of Physics at 15:06
Key Takeaways
- Scattering amplitudes act fundamentally as boundary observables at infinity, a necessity when incorporating both quantum mechanics and gravity.
- Kinematic space can be parameterized cleanly using X_ij variables derived from momentum polygons, avoiding redundant constraints from Mandelstam invariants.
- Feynman diagrams for planar trace phi-cubed theory correspond directly to triangulations of an n-gon polygon.
- Tree-level scattering amplitudes manifest locality through simple poles at X_ij = 0 and unitarity through factorization into lower-point amplitudes.
Concepts Explained18
Locality in Spacetime—The principle that physical actions and interactions occur locally in spacetime, which particle trajectory pictures attempt to make manifest.
Unitarity—The condition that quantum mechanical probabilities sum to one, represented by off-shell virtual particle contributions adding up to zero.
Celestial Holography—A framework that labels scattering amplitudes by where particles go on the celestial sphere when going out to infinity.
Celestial sphere—A geometric space representing points of scattering where amplitudes exhibit conformal symmetries of the Lorentz group.
Examples, Proofs & Derivations