Amplituhedron

In mathematics and theoretical physics (especially twistor string theory), an amplituhedron is a geometric structure introduced in 2013 by Nima Arkani-Hamed and Jaroslav Trnka.

[3][4] The connection between the amplituhedron and scattering amplitudes is a conjecture that has passed many non-trivial checks, including an understanding of how locality and unitarity arise as consequences of positivity.

The on-shell scattering process "tree" may be described by a positive Grassmannian, a structure in algebraic geometry analogous to a convex polytope, that generalizes the idea of a simplex in projective space.

[3] A polytope is the n-dimensional analogue of a 3-dimensional polyhedron, the values being calculated in this case are scattering amplitudes, and so the object is called an amplituhedron.

In a conventional perturbative approach to quantum field theory, such interactions may require the calculation of thousands of Feynman diagrams, most describing off-shell "virtual" particles which have no directly observable existence.

In contrast, twistor theory provides an approach in which scattering amplitudes can be computed in a way that yields much simpler expressions.