
How Feynman Diagrams Revolutionized Physics - furcyd
https://www.quantamagazine.org/how-feynman-diagrams-revolutionized-physics-20190514/
======
wizardforhire
For anyone interested in a deeper (but not dense) introduction to how and why
Feynman diagrams work I’ve found a lot of pleasure going through this blog
post below.

[https://www.quantumdiaries.org/2010/02/14/lets-draw-
feynman-...](https://www.quantumdiaries.org/2010/02/14/lets-draw-feynman-
diagams/)

~~~
jarvist
Chapters 0 and 1 in this book by Mattuck are also a fantastic read for a
general audience interested in what's going on 'under the hood'.
[https://www.amazon.co.uk/Feynman-Diagrams-Many-body-
Problem-...](https://www.amazon.co.uk/Feynman-Diagrams-Many-body-Problem-
Physics/dp/0486670473)

Feynman's own book 'QED: the strange theory of light and matter' is another
good read, but strangely it is a bit lacking in illustrations. (And the
illustrations that are there are a bit dry compared to Mattuck!)

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sillyquiet
PBS Space Time, as usual, has an excellent layperson's explanation of the
diagrams. [https://www.youtube.com/watch?v=fG52mXN-
uWI](https://www.youtube.com/watch?v=fG52mXN-uWI)

------
stared
Diagrams are very general and can be extrapolated from quantum field theory to
deep learning, see: [https://medium.com/@pmigdal/in-the-topic-of-diagrams-i-
did-w...](https://medium.com/@pmigdal/in-the-topic-of-diagrams-i-did-write-a-
review-simple-diagrams-of-convoluted-neural-networks-6418a63f9281)

"In particle physics, people use Feynman diagrams a lot. And these are nothing
more or less than a graphical representation of summations and integrations
over many variables. Also, as an ex-quantum physicist, I am a big fan of
tensor diagrams [...]. You can think about it as the Einstein summation
convention with no dummy indices (see Einsum in PyTorch)."

~~~
evanb
You're probably better off with some kind of Penrose graphical notation
[https://en.wikipedia.org/wiki/Penrose_graphical_notation](https://en.wikipedia.org/wiki/Penrose_graphical_notation)

~~~
stared
It’s the same.

~~~
evanb
I didn't see, for example, the circling-a-group for taking derivatives.

~~~
stared
Sure, there are other elements (derivative, (anti)symmetrization,
lowering/raising indices). The core element of summation stays the same.

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beezle
Drawing Theories Apart is an excellent book on Feynman Diagrams. You don't
have to be actively involved in nuclear or hep to understand but the material
is not for the faint of heart and a decent background in those areas goes a
long way.

[https://www.amazon.com/Drawing-Theories-Apart-Dispersion-
Dia...](https://www.amazon.com/Drawing-Theories-Apart-Dispersion-
Diagrams/dp/0226422674/ref=sr_1_5?keywords=feynman+diagrams&qid=1557847023&s=books&sr=1-5)

------
alephu5
I don't really know how you can understand Feynman diagrams without seeing how
annihilation and creation operators act on the vacuum. They are the
mathematical building blocks of qft; formally they are linear operators that
represent the creation or annihilation of particles.

If you apply an annihilation operator to a state containing no particles then
the string gets deleted from your equation. Moreover if you swap the order of
two operators you get an artifact (they're matrices after all), so a•b = b•a +
c and so in qft calculations you swap your strings of operators around until
you end up distilling it down to just a few non-vanishing artifacts that can
be calculated. There's something called wick's theorem that the result of this
process can actually be mapped onto a graph if you specify the initial and
final state.

~~~
mnl
Yeah, normal ordering and contractions, if we're expanding the fields in terms
of such operators when doing canonical quantization using Fock spaces. There's
a lot of stuff going on there. The fact that we can draw nice pictures
representing the terms of a perturbation theory doesn't mean that you can skip
a regular course on QFT to understand what practitioners mean when they use
them. Again, not stressing this while showing tree level Feynman diagrams as
if they were straight representations of particle interactions may give wrong
ideas to the unsuspecting readers.

------
aerovistae
Frustrating because it doesn't actually tell you how they work.

~~~
zinclozenge
Feynman diagrams are just pictorial representations of terms from a power
series expansion of an overall 'master' equation representing a certain
scattering process. A fairly simple one is electron positron annihilation,
which yields two photons.

~~~
gpsx
I also will expand on this.

Quantum field theory is very difficult and we can't solve many problems. We
can solve one in particular, free particles that do not interact. (By the way,
this is like solving a simple harmonic osciallator.) Feynman diagrams use the
solution to free particles as a basis - these are the lines in the diagram,
like particles moving in time. Then, we add the interactions between the
particles as a pertabative exapansion. This is what the parent comment refers
to as the power series expansion. It is expanding in the powers of the
interaction terms.

As mentioned in the video, it is not quite as simple as this however. If you
do this, you will get infinity as a result of the calculation. That is not a
very good perterbation theory. However the real discovery of physcists from
this time was renormalization. They found out you can sum many contributions
from different terms in the exapansion, corresponding to different indiviaul
feynmann diagrams, and you can make these infinities cancel out. What is magic
is that when this process is done you can write an effective theory for the
interactions that looks exactly like the original theory you started with, and
only the values of the coeffiecients are changed a little.

The magic involved here could be explained more, but in summary what it means
is that the perterbation calculation you do is valid even thought it looks
like it should be infinite. It also lets you make the simple analogy that the
lines in the diagram are real and virtual particles rather than just the non-
interacting approximation you starter with.

~~~
gpsx
I left out some important details in the above explanation. So here is part
2...

Feynman discovered another very important item, the path integral formulation
of physics. This was important for his derivation of Feynman diagrams and also
it is a good conceptual tool.

Think of basic quantum mechanics and firing an electron through a double slit
at a screen. In quantum mechanics the eletron does not have a single
trajectory from the gun to the screen. Rather, it takes all the trajectories
in parallel, like a wave. We can add the contribution as if the particle went
over each possible trajectory and this is the same as treating the electron as
if its position was given by a propogating wave. This sum over possible
histories is the interpretation of Feynmans path integrals. And it is a nice
way to think about quantum mechanics - multiple things are happening in
parallel.

Taking the example in the video of two electrons scattering off each other,
each Feynman diagram represents a possible history for the two particles,
including their trajectory and any interactions between them. These
interactdions are drawn as a connecting line, which is a "virtual particle"
being exchanged.

More specifically, the diagram doesn't represent a single history, rather it
represents all histories that have a ceratain topology, meaning here for
example one photon is exchanged between the electrons. (There is an integral
done to add up all the different ways this can happen.) To do the full
calculation, there are many diagrams that must be included. As it is a
perterbation theory, you can choose to get more accurate by include more
diagrams. The expansion parameter is basically a vertex on the diagram. The
more vertices you include, the more accurate you will be (assuming you include
all diagrams with that number of vertices).

So basically the feynman diagram is a bookkeeping mechanism to account for all
possible histories of the particles in the interaction (electon scattering
here). We sum up the contribution from all these histories to find out the
quantum amplitude for this scattering scenario. This is exactly analogous to
adding the contribution from different paths to fine the amplitude
(~probability) for our electron in the double slit experiment hitting a
particular location on the screen.

To get to this intuitive result mathematically, the perturbation expansion and
renormalization mentioned above are both involved.

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xorand
In case anybody interested in graphic lambda calculus, there are 5! X 5! =
14400 possible alternatives for the beta rewrite only. So it beats me why
among all the possible calculi in CS the lambda calculus is special. I made a
page which gives random alternatives
[http://imar.ro/~mbuliga/betarand.html](http://imar.ro/~mbuliga/betarand.html)

~~~
danharaj
Because of the Curry-Howard-Lambek correspondence.

~~~
xorand
Agree, but I don't say that lambda calculus is not interesting, I say that
there are so much more alternatives, unexplored. If we do the same with the IC
of Lafont, I think that the possible (right patterns) of rewrites (which
preserve the no of half-edges and nodes) are about 10^13.

A conjecture, which I don't know if it holds water, is that analoguous to CA,
Wolfram style, perhaps 1/3 (or anyway a significant proportion) of the 10^13
possible graph rewrite systems, alternative to IC, are Turing universal.

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melling
They promote their book after the video. Any opinions?

“Alice and Bob Meet the Wall of Fire: The Biggest Ideas in Science from Quanta
”

[https://www.amazon.com/Alice-Bob-Meet-Wall-
Fire/dp/026253634...](https://www.amazon.com/Alice-Bob-Meet-Wall-
Fire/dp/026253634X)

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andrewshadura
Sadly, despite having read about them about a dozen times, I still don't
understand how they work, or rather how to use them. Apparently, that's
because of insufficient knowledge of the relevant part of physics.

~~~
louthy
Feynman's own QED book is a fantastic introduction to QED and his diagrams

[https://www.amazon.co.uk/QED-Strange-Theory-Penguin-
Science/...](https://www.amazon.co.uk/QED-Strange-Theory-Penguin-
Science/dp/0140125051/ref=sr_1_1?crid=28BZ2MNIPKCP4&keywords=feynman+QED&qid=1557848107&s=gateway&sprefix=Feyn%2Caps%2C169&sr=8-1)

~~~
guillaumec
Yes! I just finished it. Best vulgarization book I have ever read. Not a
single equation, but still telling you exactly how the physics work, without
any hand waving. I can't recommend it enough.

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Myrmornis
I really like Quanta and I'm disappointed that they are spending resources on
creating video content (and presumably reducing the written content
accordingly). I don't know if it's obviously elitist of me (to wish to deny
people the opportunity to educate themselves via video if that's what they
like) or absurd of me to think that it could possibly be elitist to try to
retain the tradition of education-via-writing-and-reading. Anyway, I like
reading quanta, and I don't watch videos unless they are extremely special
(3b1b) or I'm in an odd mood.

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hepnewb
What about Twistors, are they the future?

~~~
musgravepeter
My perception (as a lapsed PhD physicist) is the community takes on a new
formalism when it has to i.e. there are _new_ results that can only be derived
with the new formalism. A formalism that allows slightly better derivation of
existing results does not attract attention. Twistors, Clifford algebras and
other things seem to have not met this hurdle so far.

Feynman diagrams, Riemannian geometry (General Relativity) did.

~~~
filmor
Clifford algebras are used whenever you use Gamma matrices, I think their a
well established.

~~~
eigenspace
I think the person you're replying to was talking about Geometric Algebra,
which is more of a project to reformulate all our current vector and tensor
notation in terms of Clifford algebras and to move away from using specific
representations of the algebra and instead just leverage the algebraic
properties themselves.

If you look at how most physicists use the gamma matrices, they are very
reluctant to treat them as algebraic objects and rely heavily on their matrix
representation. A proponent of GA would say this is like using the matrix

    
    
        [ 0 1
        [-1 0]
    

everywhere in your calculations instead of just using i and remembering that
i^2 = -1. Sure, it's formally equivalent but you'd still miss out on a lot of
the beauty of the complex numbers.

For what it's worth, I have a soft spot in my heart from Geometric Algebra,
but I think it still needs a lot of notational improvement before it'll ever
see any real adoption.

If you're curious about GA as it currently stands, I'd check out Geometric
Algebra for Physicists by Doran and Lasenby.

