#Amplituhedron not even wrong how to#

The Feynman diagram expansion is perturbative, and the leading order piece is always captured by tree graphs (no loops). This gives a function M of external momenta and helicities (which is spin for massless particles).

#Amplituhedron not even wrong how to#

If there is any chance to pursue our project further we need to do the reformulation for this case first.ДЇeynman diagrams give us rules for how to calculate an amplitude for any given scattering process, and these rules are very simple: draw all diagrams built from vertices given by the Lagrangian and evaluate them using certain rules. It is a very special theory sometimes referred as вЂњSimplest Quantum Field TheoryвЂќ because of its enormous amount of symmetry. In particular, I will focus on on-shell (вЂњrealвЂќ as opposed to вЂњvirtualвЂќ) scattering amplitudes of massless particles in a вЂњsupersymmetric cousinвЂќ of Quantum Chromodynamics (theory which describes strong interactions) called N=4 Super Yang-Mills theory (in planar limit). Obviously I am not going to solve this problem but rather concentrate on a much simpler problem whose solution might have some features that can be eventually generalized. The underlying motivation of my work is a very ambitious attempt to reformulate QFT using a different set of principles and see locality and unitarity emerge as derived properties. The Lagrangian formulation of QFT builds on two pillars: locality and unitarity, which means that the particle interactions are point-like and sum of the probabilities in scattering experiments must be equal to one. There are also two nice popular articles by Natalie Wolchover вЂ“ on the Amplituhedron and also the progress of understanding amplitudes in quantum gravity. For a very nice history of the field look at the blog post by Lance Dixon who recently won together with Zvi Bern and David Kosower the Sakurai prize. This has been most dramatically seen in calculation of scattering amplitudes, which are basic objects directly related to probabilities in scattering experiments. However, over the past 25 years there has been an increasing evidence that the standard definition of QFT using Lagrangians and Feynman diagrams does not exhibit simplicity and sometimes even hidden symmetries of the final result. It unifies quantum mechanics and special theory of relativity in a consistent way and it has been proven to be an extremely successful theory in countless number of cases. Our main theoretical tool in describing the microscopic world is Quantum Field Theory (QFT), developed more than 60 years ago in the hands of Dirac, Feynman, Dyson and others. To remind you, вЂњamplitudesвЂќ in quantum field theory are functions that we square to get probabilities in scattering experiments, for example that two particles will scatter and convert into two other particles.Дespite the fact that I will talk about some specific statements for scattering amplitudes in a particular gauge theory, let me first mention the big picture motivation for doing this. I am happy to do it, as the new picture for scattering amplitudes I have been looking for in last few years just recently crystalized in the object we called Amplituhedron, emphasizing its connection to both scattering amplitudes and the generalization of polyhedra. I would like to thank Sean to give me an opportunity to write about my work on his blog. For a very basic overview of Feynman diagrams in quantum field theory, see my post on effective field theory. вЂњHalfway between a popular account and a research paperвЂќ can still be pretty forbidding for the non-experts, but hopefully this guest blog post will convey some of the techniques used and the reasons why physicists are so excited by these (still very tentative) advances. Fortunately, Jaroslav is now a postdoc here at Caltech, and was willing to fill us in on a bit more of the details. Natalie WolchoverвЂ™s explanation in Quanta is a great starting point, but thereвЂ™s still a big gap between a popular account and the research paper, in this case by Nima Arkani-Hamed and Jaroslav Trnka. This is cutting-edge stuff at the forefront of modern physics, and itвЂ™s not an easy subject to grasp. It relayed the news of an intriguing new way to think about quantum field theory - a mysterious mathematical object called the Amplituhedron, which gives a novel perspective on how we think about the interactions of quantum fields. But last year a story in Quanta proved to be an exception. Usually, technical advances in mathematical physics donвЂ™t generate a lot of news buzz.