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Archive for February 14th, 2010

Let’s draw Feynman diagrams!

Sunday, February 14th, 2010

Greetings! This post turned into a multi-part ongoing series about the Feynman rules for the Standard Model and a few of its extensions. I’ll use this first post as an index for all of the parts of the series.

  1. Let’s draw Feynman diagrams! (this post)
  2. More Feynman diagrams.
  3. Introducing the muon.
  4. The Z boson and resonances.
  5. Neutrinos.
  6. The W boson, mixing things up.
  7. Meet the quarks.
  8. World of glue.
  9. QCD and confinement.
  10. Known knowns of the Standard Model. (summary)
  11. When Feynman Diagrams Fail.
  12. An idiosyncratic introduction to the Higgs.
  13. A diagrammatic hint of masses from the Higgs
  14. Higgs and the vacuum: Viva la “vev”
  15. Helicity, Chirality, Mass, and the Higgs
  16. The Birds and the Bs
  17. The spin of gauge bosons
  18. Who ate the Higgs?
  19. Unitarization of vector boson scattering
  20. Private lives of Standard Model particles (summary)

There are few things more iconic of particle physics than Feynman diagrams. These little figures of squiggly show up prominently on particle physicists’ chalkboards alongside scribbled equations. Here’s a ‘typical’ example from a previous post.

The simplicity of these diagrams has a certain aesthetic appeal, though as one might imagine there are many layers of meaning behind them. The good news is that’s it’s really easy to understand the first few layers and today you will learn how to draw your own Feynman diagrams and interpret their physical meaning.

You do not need to know any fancy-schmancy math or physics to do this!

That’s right. I know a lot of people are intimidated by physics: don’t be! Today there will be no equations, just non-threatening squiggly lines. Even school children can learn how to draw Feynman diagrams (and, I hope, some cool science). Particle physics: fun for the whole family. 🙂

For now, think of this as a game. You’ll need a piece of paper and a pen/pencil. The rules are as follows (read these carefully):

  1. You can draw two kinds of lines, a straight line with an arrow or a wiggly line:propagator2types
    You can draw these pointing in any direction.
  2. You may only connect these lines if you have two lines with arrows meeting a single wiggly line.
    QEDvertex
    Note that the orientation of the arrows is important! You must have exactly one arrow going into the vertex and exactly one arrow coming out.
  3. Your diagram should only contain connected pieces. That is every line must connect to at least one vertex. There shouldn’t be any disconnected part of the diagram.
    connected
    In the image above the diagram on the left is allowed while the one on the right is not since the top and bottom parts don’t connect.
  4. What’s really important are the endpoints of each line, so we can get rid of excess curves. You should treat each line as a shoelace and pull each line taut to make them nice and neat. They should be as straight as possible. (But the wiggly line stays wiggly!)
    wibblywobbly

That’s it! Those are the rules of the game. Any diagram you can draw that passes these rules is a valid Feynman diagram. We will call this game QED. Take some time now to draw a few diagrams. Beware of a few common pitfalls of diagrams that do not work (can you see why?):

notallowed

After a while, you might notice a few patterns emerging. For example, you could count the number of external lines (one free end) versus the number of internal lines (both ends attached to a vertex).

  • How are the number of external lines related to the number of internal lines and vertices?
  • If I tell you the number of external lines with arrows point inward, can you tell me the number of external lines with arrows pointing outward? Does a similar relation hole for the number of external wiggly lines?
  • If you keep following the arrowed lines, is it possible to end on some internal vertex?
  • Did you consider diagrams that contain closed loops? If not, do your answers to the above two questions change?

I won’t answer these questions for you, at least not in this post. Take some time to really play with these diagrams. There’s a lot of intuition you can develop with this “QED” game. After a while, you’ll have a pleasantly silly-looking piece of paper and you’ll be ready to move on to the next discussion:

What does it all mean?

(more…)

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