The traditional formulation of quantum field theory—encoded in its very name—is built on the two pillars of locality and unitarity. The standard apparatus of Lagrangians and path integrals allows us to make these two fundamental principles manifest. This approach, however, requires the introduction of a large amount of unphysical redundancy in our description of physical processes. Even for the simplest case of scalar field theories, there is the freedom to perform field redefinitions. Starting with massless particles of spin 1 or higher, we are forced to introduce even larger, gauge redundancies.

shinichiPost authorGrassmannian Geometry of Scattering Amplitudes

by Nima Arkani-Hamed, Jacob Bourjaily, Freddy Cachazo, Alexander Goncharov, Alexander Postnikov, Jaroslav Trnka

Outlining a revolutionary reformulation of the foundations of perturbative quantum field theory, this book is a self-contained and authoritative analysis of the application of this new formulation to the case of planar, maximally supersymmetric Yang–Mills theory. The book begins by deriving connections between scattering amplitudes and Grassmannian geometry from first principles before introducing novel physical and mathematical ideas in a systematic manner accessible to both physicists and mathematicians. The principle players in this process are on-shell functions which are closely related to certain sub-strata of Grassmannian manifolds called positroids – in terms of which the classification of on-shell functions and their relations becomes combinatorially manifest. This is an essential introduction to the geometry and combinatorics of the positroid stratification of the Grassmannian and an ideal text for advanced students and researchers working in the areas of field theory, high energy physics, and the broader fields of mathematical physics.

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1. Introduction

The traditional formulation of quantum field theory—encoded in its very name—is built on the two pillars of locality and unitarity. The standard apparatus of Lagrangians and path integrals allows us to make these two fundamental principles manifest. This approach, however, requires the introduction of a large amount of unphysical redundancy in our description of physical processes. Even for the simplest case of scalar field theories, there is the freedom to perform field redefinitions. Starting with massless particles of spin 1 or higher, we are forced to introduce even larger, gauge redundancies.

This has been seen dramatically at strong coupling in gauge/gauge and gauge/gravity dualities. The past decade has uncovered further remarkable new structures in field theory even at weak coupling, seen in the properties of scattering amplitudes in gauge theories and gravity. The study of scattering amplitudes is fundamental to our understanding of field theory, and fueled its early development in the hands of Feynman, Dyson, and Schwinger among others. It is therefore surprising to see that even here, by committing so strongly to particular, gauge-redundant descriptions of the physics, the usual formalism is completely blind to astonishingly simple and beautiful properties of the gauge-invariant physical observables of the theory.Over the past few decades, there has been a growing realization that these redundancies hide amazing physical and mathematical structures lurking within the heart of quantum field theory.

Many of the recent developments have been driven by an intensive exploration of N = 4 supersymmetric Yang–Mills (SYM) in the planar limit. The all-loop integrand for scattering amplitudes in this theory can be determined by a generalization of the BCFW recursion relations, in a way that is closely tied to remarkable new structures in algebraic geometry, associated with contour integrals over the Grassmannian G(k, n). This makes both the conformal and long-hidden dual conformal invariance of the theory (which together close into the infinite-dimensional Yangian symmetry) completely manifest. It is remarkable that a single function of external kinematical variables can be interpreted as a scattering amplitude in one space-time, and as a Wilson loop in another. Each of these descriptions makes a commitment to locality in its own space-time, making it impossible to see the dual picture.

shinichiPost authorNima Arkani-Hamed

Wikipedia

https://en.wikipedia.org/wiki/Nima_Arkani-Hamed

Nima Arkani-Hamed (Persian: نیما ارکانی حامد; born April 5, 1972) is an American-Canadian theoretical physicist, with interests in high-energy physics, quantum field theory, string theory, cosmology and collider physics. Arkani-Hamed is a member of the permanent faculty at the Institute for Advanced Study in Princeton, New Jersey. He is also director of The Center for Future High Energy Physics (CFHEP) in Beijing, China.

shinichiPost author宇宙の終わりに何が起こるのか

by ケイティ・マック

http://www.kushima.org/?p=65884

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アルカニ=ハメドは、粒子どうしの相互作用を、まったく新しい枠組みを使って計算する方法を構築しているところだ。その枠組みは、空間と時間がまったく含まれない、抽象的な数学からスタートする。彼の取り組みはまだ初期段階で、これまでのところ、実験結果よりも、ある種の理想化された系のほうによくあてはまる。だが、これがうまくいったとすると、それほどショッキングなことは他にないだろう。

shinichiPost author数学に魅せられて、科学を見失う――物理学と「美しさ」の罠

by ザビーネ・ホッセンフェルダー

http://www.kushima.org/?p=65909

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「誰もバラ色の人生なんて約束しませんでしたよ。これはリスクのある仕事なのです」（ニマ・アルカニ=ハメド）

4. Cracks in the Foundations

In which I meet with

Nima Arkani-Hamedand do my best to accept that nature isn’t natural, everything we learn is awesome, and that nobody gives a fuck what I think.**

So there’s no experiment and you just sit around and talk about beauty and elegance and mathematical loveliness. And it sounds like sociological bullshit. I think this impression is just completely wrong—but completely wrong for an interesting reason. That reason makes us in high-energy physics different from most other parts of science.

It’s true that in most other parts of science what’s needed to check whether ideas are right or wrong are new experiments. But our field is so mature that we get incredible constraints already by old experiments. The constraints are so strong that they rule out pretty much everything you can try. If you are an honest physicist, 99.99 percent of your ideas, even good ideas, are going to be ruled out, not by new experiments but already by inconsistency with old experiments. This is what really makes the field very different, and what gives us an internal notion of right and wrong before new experiments. So, quite contrary to the sense that this skeptical layperson would get, the idea that you can just make up crap is wrong. It’s an incredible struggle.