Particle interactions calculated with a single term all done *by hand*?! That’s crazy. In case you have nothing to base calculating particle interactions in quantum field theory on, just imagine having thousands of puzzle pieces scattered everywhere to suddenly, without all the pesky pieces, having a single, unified picture. All it takes is some new thinking and a little geometry.

In this new model, physicists describe the universe by an amplituhedron, an infinite-dimensional geometric object. The volume of this object is equal to the scattering amplitude—the holy grail of particle physics—which physicists at the Large Hadron Collider use to describe particle interactions. In some **amplitu**hedrons the amplitudes can be calculated directly. In others diagrams called “twistors” are needed.

What’s more, they’ve found the solution to everything. The volume of an infinite-sided “master amplituhedron” represents *the amplitudes of all physical processes*. The italics are supposed to impress you. Interactions between a finite number of processes, what us humans normally consider, are contained on various faces. Interesting to me, but probably not to anyone else, is that the master amplituhedron simplifies to a circle in 2D.

Amplituhedron representing an 8-gluon particle interaction, which normally needs ~500 pages of algebra.

The amplituhedron removes locality and unitarity. Particles that aren’t near either other in space or time can interact (what?) and the sum of the probabilities for all possible particle positions doesn’t have to be 1 (what?!). That works out for gravity though, which explodes—yes, explodes—in equations with locality and unitarity. Connecting gravity to particle physics is a big deal—no one’s been able to do it yet. Jacob Bourjaily, one of the researchers, described this method as “a starting point to ultimately describing a quantum theory of gravity.”

Nima Arkani-Hamed, the lead author (the main man, the head honcho), gave a talk about amplituhedrons at the SUSY 2013 conference, which is posted online. Warning: the talk is *very* technical, but interesting nonetheless (if only to watch a man in shorts and a shirt two sizes too large give a spitfire professional talk). Although, in the talk he says amplituhedrons can be “explained to a smart junior high school student,” which left me feeling like a stupid graduate student.

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*Related*

There is a jewel at the heart of financial markets – the stockMarkethedron – related to amplituhedron.

http://arxiv.org/abs/1402.1281