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#feynman

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Paul Balduf

Together with Simone Hu, we have a new #preprint in theoretical #physics, or rather #mathematics.
The upshot is that there is a certain formulation of #Feynman integrals that is useful in a class of #quantum field theories (namely, 1-dimensional topological directions in holomorphic-topological theories). The integrand of these integrals is what we call "topological form".
On the other hand, there is a family of integrals that detects cohomology classes in the odd graph complex. That means, they find out whether some graph can be generated by shrinking edges in a certain way. The integrand in these integrals is called "Pfaffian form".
In our new preprint, we prove that the Pfaffian form and the topological form are the same.
arxiv.org/abs/2503.09558

arXiv.orgThe Topological form is the Pfaffian formFor a given graph $G$, Budzik, Gaiotto, Kulp, Wang, Williams, Wu, Yu, and the first author studied a ''topological'' differential form $α_G$, which expresses violations of BRST-closedness of a quantum field theory along a single topological direction. In a seemingly unrelated context, Brown, Panzer, and the second author studied a ''Pfaffian'' differential form $ϕ_G$, which is used to construct cohomology classes of the odd commutative graph complex. We give an explicit combinatorial proof that $α_G$ coincides with $ϕ_G$. We also discuss the equivalence of several properties of these forms, which had been established independently for both contexts in previous work.
Public
Paul Balduf

In #physics, #quantum field theory is used to describe the behavior of elementary particles. #Feynman diagrams are used to visualize, and compute, the "elementary" processes that can happen. However, the processes that really occur in nature are a sum of infinitely many Feynman diagrams. Of course, in an actual computation, one can only include finitely many processes, and all the other ones need to absorbed into some "effective" parameters, such as effective charges. This is called #renormalization, and it involves a freedom regarding how exactly one defines the effective parameters. Two renormalization schemes are common in high energy physics: In "kinematic renormalization", one defines the effective parameters as the actually measured values of a certain scattering process. In "minimal subtraction", one chooses the effective parameters such that the computation is as easy as possible, regardless of what the parameters mean concretely.
Certain infinite sums of Feynman diagrams, called "rainbows" (see picture), had been computed in minimal subtraction 30 years ago. In a recent preprint arxiv.org/abs/2503.02079 I computed the analogous sums in the minimal subtraction scheme. The solution is structurally similar to the known one, but they involve slightly more complicated functions.
The sum of rainbows by itself is not a physically relevant observable. But since it is one of the few infinite classes of Feynman diagrams that can be solved exactly, it is often used as a model to describe qualitative features, such as how quickly these sums grow if one includes more and more terms.

The first three terms in an infinite sum of rainbow diagrams. These diagrams consist of one horizontal line, and an increasing number of nested arcs that connect to the base line on both ends. Each line represents an elementary particle, each meeting point of multiple lines is an elementary interaction.
Continued thread
Public
mau 🏳️‍🌈#EndFossilFuels

"...gravitation has relatively few practical applications. (...) working out the motions of the satellites and (...) also, modernly, to calculate the predictions of the planet's position, which have great utility for astrologers to publish their predictions and horoscopes in the magazines.

That's the strange world we live in, that all the advances in understanding are used only to continue the nonsense which has existed for two thousand years."

#Feynman
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Victoria Stuart 🇨🇦 🏳️‍⚧️

Due to the influence of gravity, the Earth's core is 2.5 years younger than its crust
fermatslibrary.com/s/the-young

* scientists revisit claim by Richard Feynman
* famously suggested, 1960s Caltech lecture, gravitational time dilation (general relativity)
* would make the Earth's core younger than crust by "day or 2"
* gen. concept correct h/e estimate wrong
* pedagogical value: any number/observation, by whomever, must be critically examined

Fermat's LibraryFermat's Library | A Relational Model of Data for Large Shared Data Banks annotated/explained version.Fermat's Library is a platform for illuminating academic papers.
#FermatsLibrary#Feynman#physics
Public *
The Krononaut Moon Project 🌑

 
Richard Feynman talks about light. 6-min.

❛❛ For his contributions to the development of #quantum #electrodynamics, #Feynman received the #NobelPrize in #Physics in 1965 jointly with Julian Schwinger and Shin'ichirō Tomonaga. ❜❜ #Wikipedia

🔗 youtube.com/watch?v=FjHJ7FmV0M 2007 Nov 02
🔗 Wikipedia.org/wiki/Richard_Fey … #RichardFeynman
🔗 Wikipedia.org/wiki/Light … #Light

YouTubeRichard Feynman talks about lightBy sdfhsfh
#Community#TimeTravel#Research
Continued thread
Public
Chuck Darwin

#Figueiredo sensed the need for some new magic firsthand during the waning months of the pandemic.

She was struggling with a task that has challenged physicists for more than 50 years:

predicting what will happen when quantum particles collide.

In the late 1940s, it took a yearslong effort by three of the brightest minds of the post-war era
— Julian #Schwinger, Sin-Itiro #Tomonaga and Richard #Feynman
— to solve the problem for electrically charged particles.

Their eventual success would win them a Nobel Prize.

Feynman’s scheme was the most visual, so it came to dominate the way physicists think about the quantum world.

When two quantum particles come together, anything can happen.

They might merge into one, split into many, disappear or any sequence of the above.

And what will actually happen is, in some sense, a combination of all these and many other possibilities.

Feynman diagrams keep track of what might happen by stringing together lines representing particles’ trajectories through space-time.

Each diagram captures one possible sequence of subatomic events
and gives an equation for a number,
called an “amplitude,”
that represents the odds of that sequence taking place.

Add up enough amplitudes, physicists believe, and you get stones, buildings, trees and people.

“Almost everything in the world is a concatenation of that stuff happening over and over again,” Arkani-Hamed said.

“Just good old-fashioned things bouncing off each other.”

There’s a puzzling tension inherent in these amplitudes
— one that has vexed generations of quantum physicists going back to Feynman and Schwinger themselves.

One might spend hours at a chalkboard sketching Byzantine particle trajectories and evaluating fearsome formulas only to find that terms cancel out
and complicated expressions melt away to leave behind extremely simple answers
— in a classic example,
literally the number 1.

“The degree of effort required is tremendous,” Bourjaily said.

“And every single time, the prediction you make mocks you with its simplicity.”

Figueiredo had been wrestling with the strangeness of the situation when she attended a talk by #Arkani-#Hamed,
a leading theoretical physicist at the IAS who has spent years seeking a new way of getting the answers without Feynman diagrams.

She found her way to a series of his lectures on YouTube, in which he showed how
— in special cases
— one could jump straight to the amplitude of a certain outcome of a particle collision without worrying about how the particles moved through space.

Arkani-Hamed’s shortcuts, which involved reverse-engineering answers that satisfy certain fundamental logical requirements,
confirmed Figueiredo’s suspicions that alternative methods were out there.

“By asking for these very simple things you could just get the answer.

That was definitely striking,” she said.

She began to regularly make the half-hour walk from Princeton’s campus to the IAS to work with Arkani-Hamed,
a force of nature who runs on Diet Coke and an inexhaustible enthusiasm for physics.

Arkani-Hamed and his collaborators aspire to bring about a conceptual revolution of the sort that rocked physics in the late 1700s.

Joseph-Louis #Lagrange didn’t discover any forces or laws of nature, but every physicist knows his name.

He showed that you could predict the future without laboriously calculating actions and equal-and-opposite reactions in the style of Isaac Newton.

Instead, Lagrange learned to predict the path an object will follow by considering the energies that different paths require and identifying the easiest path.

Lagrange’s method, despite seeming like a mere mathematical convenience at the time,
loosened the straitjacket of Newton’s mechanistic view of the universe as a sequence of falling dominos.

Two centuries later, Lagrange’s approach provided Feynman with a more flexible framework that could accommodate the radical randomness of quantum mechanics.

Now many amplitudes researchers hope a reformulation of quantum physics will set the stage for the next physics revolution,
a theory of quantum gravity and the origin of space-time.

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