Finally The Amplituhedron Paper

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In summary: However, the amplitudes computed this way are not really "amplitudes" in the classical sense, but rather quantities that are closely related to the Feynman propagators. They are not really "scattering amplitudes" either, in the sense that they are not really the amplitudes that determine the scattering cross section. They are more accurately called "transverse momentum amplitudes."
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http://arxiv.org/abs/1312.2007

The Amplituhedron

Nima Arkani-Hamed, Jaroslav Trnka
(Submitted on 6 Dec 2013)
Perturbative scattering amplitudes in gauge theories have remarkable simplicity and hidden infinite dimensional symmetries that are completely obscured in the conventional formulation of field theory using Feynman diagrams. This suggests the existence of a new understanding for scattering amplitudes where locality and unitarity do not play a central role but are derived consequences from a different starting point. In this note we provide such an understanding for N=4 SYM scattering amplitudes in the planar limit, which we identify as ``the volume" of a new mathematical object--the Amplituhedron--generalizing the positive Grassmannian. Locality and unitarity emerge hand-in-hand from positive geometry.
 
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This is a beautiful, important, albeit late paper (eg most of the main insights have been known for months now). One that really has a lot of different great physicists stamp on it. It's hard not to notice Maldecena, Witten and Cachazo's distinctive and idiosyncratic insights in the structure of the insights.

I happen to believe the previous generalization in this program was arguably more important (the positive Grassmanian papers) but this is nevertheless a clear step forward. I also happen to believe there is yet another fundamental generalization that remains to be discovered and that underlies the move from from the planar limit (and one that generalizes to arbitrary renormalizations).

In terms of research directions, there should be a legion of graduate students working on specific examples.
 
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Okay, let us assume this is a fantastic new discovery. Is it fair to ask "where is the beef?" If this is a great new way to compute amplitudes then is the technique being applied to say QED computations, QCD phenomenology? If it is being applied, does it get the right answers?
 
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Yes. These techniques and their precursors were originally used several years ago to compute amplitudes for QCD background estimation at the LHC. They drastically simplify the amount of algebraic work necessary to calculate certain diagrams (with large amounts of incoming particles). So yes, the answers are correct.
 
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Related to Finally The Amplituhedron Paper

What is the Amplituhedron?

The Amplituhedron is a geometric object that was first introduced in the "Finally the Amplituhedron Paper" in 2013. It is a new way of understanding and calculating particle interactions in quantum field theory.

What is the significance of the Amplituhedron?

The Amplituhedron has the potential to revolutionize how we approach particle physics and could lead to a deeper understanding of the fundamental laws of nature. It also has the potential to simplify and streamline complex calculations in quantum field theory.

How does the Amplituhedron differ from traditional methods of calculating particle interactions?

Traditional methods of calculating particle interactions involve complicated equations and diagrams. The Amplituhedron, on the other hand, uses a geometric approach that is based on the idea that the universe can be described by a single geometric object.

What are the implications of the "Finally the Amplituhedron Paper" for the future of physics?

The "Finally the Amplituhedron Paper" has opened up new avenues for research and has the potential to greatly advance our understanding of the universe. It could also potentially lead to new technologies and applications in the future.

What are some potential criticisms of the Amplituhedron theory?

Some critics argue that the Amplituhedron is too abstract and does not provide a complete solution to particle interactions. Others argue that it is too early to determine the true implications and usefulness of the theory. Further research and experimentation are needed to fully understand the potential limitations of the Amplituhedron.

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