LAUSR

Scattering amplitudes are the bread and butter of quantum field theory. notion that space and time are fundamental components of reality...” In this short article, we will not get as far as challenging the notions of space and time, but we will give some explanation as to the nature and significance of the amplituhedron both in physics and mathematics—where it arises as a natural generalization of the subject of total positivity for Grassmannians. Let us begin with the origin of these ideas in the physics of scattering amplitudes. For any particular quantumfield theory, the probability for some number of particles to ‘scatter’ and produce some number of others is encoded by a function called the (scattering) amplitude for that process. These functions depend on all the observable numbers labeling the states involved in the process—in particular, momenta and helicity. Amplitudes can (often) be determined perturbatively according to the Feynman ‘loop’ expansion. At leading order, they are rational