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11:30 am | 10 DEC 2018
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Scattering Amplitudes and the Positive Grassmannian
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Scattering of elementary particles
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Theorist's perspective What happens during scattering experiment?
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New picture: on-shell diagrams Remarkable connection to mathematics
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Motivation
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Elementary particles and forces
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Quantum field theory
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Scattering amplitude
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Perturbative expansion
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Feynman diagrams
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Search for new physics
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Amplitudes of gluon's
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Parke-Taylor formula
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Amplitudes as a new field
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Problem with Feynman diagrams
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New objects
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Kinematics of massless particles
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Fundamental amplitudes
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Definition of on-shell diagrams
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On-shell diagrams
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Amplitudes from on-shell diagrams
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Simple examples
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Simplicity revealed
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Identity moves
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Precise statement
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Permutations
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New look at permutations
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Identity moves
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Yang-Baxter moves
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Reduced information
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Positive Grassmannian
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Positive matrices
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Face variables
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Perfect orientation
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Boundary measurement
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Entries of matrix
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Positive matrix
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Edge variables
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Cell in the Positive Grassmannian
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Example of configuration
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Example of stratification
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Relation to permutations
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Boundary operator
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Stratification of the positive Grassmannian
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Summary of positive Grassmannian
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Connection to cluster algebras
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Seed and mutation
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Square-move
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Surprising connection
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Connection
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Cluster transformation
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Momentum conservation
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Geometry of delta function
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Logarithmic form
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Derivation: starting with 3pt
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Amalgamation procedure
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New procedure
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Conclusion
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Summary
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Amplituhedron
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Non-planar on-shell diagrams
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Resources
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Thank you!
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Amplituhedron
Description:
Explore the fascinating world of scattering amplitudes and their connection to the positive Grassmannian in this comprehensive lecture. Delve into the theoretical foundations of particle physics, starting with elementary particles and forces, and progressing through quantum field theory and scattering amplitudes. Discover the limitations of traditional Feynman diagrams and learn about innovative approaches like on-shell diagrams. Examine the mathematical underpinnings, including permutations, positive matrices, and the stratification of the positive Grassmannian. Investigate the surprising connections to cluster algebras and explore advanced concepts such as the Amplituhedron. Gain insights into cutting-edge research in theoretical physics and mathematics, with discussions on non-planar on-shell diagrams and resources for further study.

Scattering Amplitudes and Positive Grassmannian by Jaroslav Trnka

International Centre for Theoretical Sciences
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#Science #Physics #Theoretical Physics #Scattering Amplitudes #Quantum Mechanics #Quantum Field Theory #Mathematics #Cluster Algebras
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11:30 am | 10 DEC 2018