The SAGEX review on scattering amplitudes Chapter 7: Positive geometry of scattering amplitudes

Scattering Amplitudes and the Positive Grassmannian

N. Arkani-Hamed, J. Bourjaily, F. Cachazo, A. Goncharov, A. Postnikov, and J. Trnka a School of Natural Sciences, Institute for Advanced Study, Princeton, NJ b Department of Physics, Harvard University, Cambridge, MA c Perimeter Institute for Theoretical Physics, Waterloo, Ontario, CA d Department of Mathematics, Yale University, New Haven CT e Department of Mathematics, Massachusetts Institute...

Calculation of the Scattering Amplitudes

It is well known that the high order calculations of the observables within the perturbation theory has the serious difficulties (especially, if we take into account the polarization effects). Method of the direct calculation of amplitudes simplifies these calculations essentially. There is an even number (2N) of fermions in initial and final state for any reaction with Dirac particles. Therefo...

TASI Lectures on Scattering Amplitudes

Tree Scattering Amplitudes *

The spin-4/3 fractional superstring is characterized by a chiral algebra involving a spin-4/3 current on the world-sheet in addition to the energy-momentum tensor. These currents generate physical state conditions on the fractional superstring Fock space. Scattering amplitudes of these physical states are described which satisfy both spurious state decoupling and cyclic symmetry (duality). Exam...

Nonperturbative Calculation of Scattering Amplitudes

A method for the nonperturbative calculation of scattering amplitudes and cross sections is discussed in the context of light-cone quantization. The Lanczos-based recursion method of Haydock is suggested for the computation of matrix elements of the resolvent for the light-cone Hamiltonian, from which the T -matrix can be constructed. The scattering of composite particles is handled by a genera...