Grunnlagt av [[Nima Arkani-Hamed]], når han oppfant/oppdaget [[Amplituhedron]]et. Han er også glad i å si at [[Space-time is doomed]]. Først hørt om av meg på [[4gravitons]]. ### MOC - [[Spinor-helicity-formalismen]] - [[MHV-amplituder]] - [[Parke-Taylor-formelen]] - [[Amplituhedron]] - [[Space-time is doomed]] - [[N=4 Super Yang-Mills]] ### Watchlist - Fra [School on Modern Amplitude Methods for Gauge and Gravity Theories 2023](https://www.youtube.com/playlist?list=PLg0_ydgtbHGFRzPmMURjPrZdyv_qdVl8c) - Først: [Jaroslav Trnka: Overview of scattering amplitudes](https://youtu.be/rcGVL_S3Hwc?si=9tQnNDIoo0OvOWaD) (5 parts) - Så: [Nima Arkani-Hamed: Big New Accelerators and the Future of Particle Physics](https://www.youtube.com/live/LIJb7SOBdcc?si=P73UJ2QGTBuAqHue) (Colloquium) - Deretter (som belønning): [Nima Arkani-Hamed: Advanced topics in amplitudes](https://youtu.be/lJwn4R3PeNc?si=6MS2oZtjoATdvuVS) (5 parts) - Og så er jeg det kanskje tid for å begynne å lese [The Elvang/Huang Primer](https://arxiv.org/pdf/1308.1697.pdf)! ### Historie Oppdagelsen som ledet til dette fagfeltet kom fra utregningen av gluon-gluon scattering i 1985, run-of-the-mill-utregninger ment til å definere standardmodellbakgrunnen for eksperimentalister til å lete etter ny fysikk på toppen av. Utregningen av $gg \rightarrow gggg$ (6 point scattering, fordi det er seks vertices i slike [[Feynmanndiagrammer]]) krevde 220 Feynmanndiagrammer *bare for tree level*; utregningen bar over mer enn 100 sider, og resultatet ble publisert som én gigantisk formel. Men innen et år innså forfatterne at uttrykket lot seg forenkle, ned til dette enkle uttrykket ($A_6$ fordi 6-point): > $A_6 = <12>^4/<12><23><34><45><56><61>\, .$ Ser du mønsteret? (Én lt;12>$ kansellerer mellom teller og nevner, men strukturen blir tydeligere når man inkluderer den.) [Jaroslav Trnka](https://youtu.be/rcGVL_S3Hwc?si=fZC_RwYj_th-BJX-&t=2445): > Once you see this structure you can immediately try to generalize it to any number of gluons, and you will indeed succeed: for certain special gluon amplitudes (hvilke? svar: [[MHV-amplituder]]) you can write a formula for the scattering of an arbitrary number of gluons. Denne formelen er i dag kjent som [[Parke-Taylor-formelen]], og benytter [[Spinor-helicity-formalismen]]. [Trnka](https://youtu.be/rcGVL_S3Hwc?si=e6wi2dyktmyR6TER&t=2502): > This is just tree level. So then, the [progress started at 1 loop in the early 1990's](https://www.sciencedirect.com/science/article/abs/pii/0550321394901791) by [Zvi Bern](https://en.wikipedia.org/wiki/Zvi_Bern) and [Lance Dixon](https://en.wikipedia.org/wiki/Lance_J._Dixon) and [David Kosower](https://physics.aps.org/authors/david_a_kosower) when they used some improvement of these methods, called unitarity methods. ### Intuisjon God forklaring på hvorfor vi får denne enorme forskjellen mellom [[Feynmanndiagrammer]] og [[Parke-Taylor-formelen]], fra [Trnka](https://youtu.be/rcGVL_S3Hwc?si=xcbdTuf5Xj-N8Nz8&t=2548): > Can we see how the cancellation happens in Feynman diagrams to give this formula? Very hardly. Now, the reason for that is basically in the core of these modern amplitude methods, because the problem is in the way we describe particles with spin. Particles with spin, in the quantum field theory, we describe using polarization vectors. But the polarization vectors don't really describe *two* helicities of the massless particles, but have more degrees of freedom in it (sic). We have to then impose certain conditions to remove these extra degrees of freedom. Now, each Feynman diagram is not invariant under these transformations, the gauge invariance that we impose, only the amplitude is. So, these individual terms (*points at the number 220*) kind of suffer from this, kind of, *baggage* of additional stuff which must cancel in the end. And this formula (*points at [[Parke-Taylor-formelen]]*) is directly a formula for the amplitude, so it doesn't have this extra redundancy that individual Feynman diagrams do have. > > Now, the lessons from this calculation was, in order to reveal simplifications of the amplitudes, and then also develop methods which would directly give this simple formula (...) is to fix the external states, the spin structure—helicities (...) and once you do it, then the formulas becomes (*sic*) extremely simple for the final amplitude. But this is something which is invisible in the Feynman diagrams, because the Feynman diagrams are designed to work for any helicity, or any spins of external states.