The Amplituhedron: the Geometry of Quantum Field Theory
The Amplituhedron: the Geometry of Quantum Field Theory Jacob Bourjaily Harvard University, Cambridge, Massechusetts The basic mathematical framework in which we understand and describe the laws of Nature today, quantum field theory, is as ubiquitous and important to modern physics as the calculus was to Newtonian dynamics. And just like the calculus during the century after Newton, quantum field theory is still considered very difficult by many, and continues to surprise us all. Despite the essential correctness of the description of quantum field theory given to us by Feynman, there remains a vast discrepancy between the difficulty of making predictions for experiments, and the near-ubiquitous, surprising simplicity of the predictions ultimately made. Recent years have witnessed the emergence of a completely new formulation of quantum field theory based exclusively on physically observable data. While mathematically equivalent to the traditional formulation, this new framework has proven dramatically more efficient—making computations that were once infeasible even using supercomputers, now routinely done on one side of a napkin. In this new description, experimental observables are computed as volumes of jewel-like regions in an abstract space, dubbed the amplituhedron. After reviewing the way quantum field theory is largely understood (and universally taught) today, I will describe the essential insights and discoveries made in the past decade, leading to the present revolution in our understanding of the mathematical structure at the heart of quantum field theory.
Jacob Bourjaily is a Junior Fellow in the Harvard Society of Fellows and a Member of the Center for the Fundamental Laws of Nature in the Department of Physics at Harvard University. He has spent the past several years working directly on the emerging reformulation of quantum field theory, contributing to many research articles on the subject including the discovery of recursion relations for scattering amplitudes valid to all orders of perturbation theory. Popular accounts of this work have appeared in Nature, Nature Physics, and Quanta Magazine. Dr Bourjaily began his career as an undergraduate at the University of Michigan, graduating with highest honors in Physics and Mathematics in 2005. He was awarded a Marshall Scholarship to study Mathematics at Cambridge University, earning a Masters of Advanced Study in 2006. He subsequently returned to the US to complete his graduate work at Princeton University, earning his PhD in 2011 under the supervision of Nima Arkani-Hamed at the Institute for Advanced Study.
Jacob Bourjaily is a Junior Fellow in the Harvard Society of Fellows and a Member of the Center for the Fundamental Laws of Nature in the Department of Physics at Harvard University. He has spent the past several years working directly on the emerging reformulation of quantum field theory, contributing to many research articles on the subject including the discovery of recursion relations for scattering amplitudes valid to all orders of perturbation theory. Popular accounts of this work have appeared in Nature, Nature Physics, and Quanta Magazine. Dr Bourjaily began his career as an undergraduate at the University of Michigan, graduating with highest honors in Physics and Mathematics in 2005. He was awarded a Marshall Scholarship to study Mathematics at Cambridge University, earning a Masters of Advanced Study in 2006. He subsequently returned to the US to complete his graduate work at Princeton University, earning his PhD in 2011 under the supervision of Nima Arkani-Hamed at the Institute for Advanced Study.
