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Amplituhedron
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Scattering Amplitudes and Positive Grassmannian by Jaroslav Trnka
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- 1 11:30 am | 10 DEC 2018
- 2 Scattering Amplitudes and the Positive Grassmannian
- 3 Scattering of elementary particles
- 4 Theorist's perspective What happens during scattering experiment?
- 5 New picture: on-shell diagrams Remarkable connection to mathematics
- 6 Motivation
- 7 Elementary particles and forces
- 8 Quantum field theory
- 9 Scattering amplitude
- 10 Perturbative expansion
- 11 Feynman diagrams
- 12 Search for new physics
- 13 Amplitudes of gluon's
- 14 Parke-Taylor formula
- 15 Amplitudes as a new field
- 16 Problem with Feynman diagrams
- 17 New objects
- 18 Kinematics of massless particles
- 19 Fundamental amplitudes
- 20 Definition of on-shell diagrams
- 21 On-shell diagrams
- 22 Amplitudes from on-shell diagrams
- 23 Simple examples
- 24 Simplicity revealed
- 25 Identity moves
- 26 Precise statement
- 27 Permutations
- 28 New look at permutations
- 29 Identity moves
- 30 Yang-Baxter moves
- 31 Reduced information
- 32 Positive Grassmannian
- 33 Positive matrices
- 34 Face variables
- 35 Perfect orientation
- 36 Boundary measurement
- 37 Entries of matrix
- 38 Positive matrix
- 39 Edge variables
- 40 Cell in the Positive Grassmannian
- 41 Example of configuration
- 42 Example of stratification
- 43 Relation to permutations
- 44 Boundary operator
- 45 Stratification of the positive Grassmannian
- 46 Summary of positive Grassmannian
- 47 Connection to cluster algebras
- 48 Seed and mutation
- 49 Square-move
- 50 Surprising connection
- 51 Connection
- 52 Cluster transformation
- 53 Momentum conservation
- 54 Geometry of delta function
- 55 Logarithmic form
- 56 Derivation: starting with 3pt
- 57 Amalgamation procedure
- 58 New procedure
- 59 Conclusion
- 60 Summary
- 61 Amplituhedron
- 62 Non-planar on-shell diagrams
- 63 Resources
- 64 Thank you!
- 65 Amplituhedron
