# Feynman diagrams in three dimensions

Is there such a thing as an extension of Feynman diagrams into three dimensions?

Canonical Feynman diagrams use one space and one time dimension to visualize processes involving elementary particles in space-time. This is very convenient for presenting them on a two-dimensional surface, such as in an academic paper.

It seems to me that with computer displays one could now employ two space and one time dimension in three-dimensional Feynman diagrams, which could be rotated on a computer screen, etc. I'm sure that this is technically feasible. I am less sure that there are relevant processes whose presentation would sufficiently gain in substance from showing two spacial dimensions instead of one, so three-dimensional Feynman diagrams (or whatever one would call those) may amount to a solution without a problem.

In terms of answers to the question I would appreciate pointers to academic papers or visualization tools, if there are any.

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Cool link by the way. "The Visual Display of Quantitative Information" had quite an impact on how I plot things. – delete000 Mar 8 '13 at 9:27
keyword "non-planar Feynman diagrams". – NikolajK Mar 8 '13 at 9:42
The lines represent 4-momenta and the math done with them (conservation and integration) work over all spacial dimensions. The two-dimensional display is merely for convenience of presentation on the page or blackboard. – dmckee Mar 8 '13 at 17:38
@dmckee agreed. In your terminology my question could be rephrased as: Are there situations when it is (or would be) convenient to present those 4-momenta in a three-dimensional display? – Drux Mar 8 '13 at 18:36

The main purpose of the space and time dimensions in Feynman diagrams is that the space dimension represents all possible spacial dimensions. 3D plots (which I assume you mean give two dimensions to space and one to time) would really only serve to give extra space on the diagram for interactions that would otherwise not fit on the page or become unreadable due to so may lines being close together. But honestly I've never seen a diagram so complicated as to need this extra space. So there's nothing really wrong with your idea, it just might not be necessary at this point.

It's important to remember that Feynman diagrams aren’t literally diagrams of the interaction taking place, but another way to represent the mathematics of the interaction. Adding extra spacial dimensions to the interaction shouldn't change the Feynman diagram.

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Thx, that's illuminating: "the space dimension represents all possible spacial dimensions" – Drux Mar 8 '13 at 11:10
"I've never seen a diagram so complicated as to need this extra space" Maybe this one? :) – Michael Brown Mar 8 '13 at 11:41
also when strings are represented by feynman type diagrams the string dimension is shown projected in the plane. It is possible that for complicated diagrams a third dimension would be useful:slimy.com/~steuard/research/StringIntro/slide22.html – anna v Mar 8 '13 at 12:09

Feynman diagrams are useful because the particles appearing in the drawings are one-dimensional (points).

String theory offers higher-dimensional extensions of Feynman diagrams, where, for example, instead of a particle decay or collision that looks like the letter "Y" (Feynman diagram), there is a particle decay or collision that looks like a pair of pants (a world sheet in String Theory).

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+1 I would think this is basically right (although I'm not an expert). Not sure why somebody gave you -1. – Keep these mind Mar 18 '14 at 19:16
+1 if you can you add a (link to an) corresponding image. Thx. – Drux Mar 18 '14 at 19:50

## protected by Qmechanic♦Mar 18 '14 at 20:13

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