### Silly Symmetry Factors

24Apr07

A few months ago some of the Part III students were having a good time calculating the symmetry factors of silly Feynman diagrams. Perhaps there are others out there who would be amused by the game.

References

For those who don’t spend much time thinking about symmetry factors, section 9 of Mark Srednicki’s QFT book is very good (as is the rest of the book). An accessible paper that goes into the nitty-gritty is “A General Expression for Symmetry Factors of Feynman Diagrams,” by Palmer and Carrington.

How to LaTeX Feynman Diagrams

The diagrams below were generated using the Windows build of JaxoDraw, a java-based interface for the Axodraw LaTeX package. My understanding is that Peskin and Schroeder‘s feynman diagrams were made using Axodraw. JaxoDraw allows you to draw diagrams on a graphic user interface and then export as an image file or as LaTeX code.

The Rules

All hanging lines are external scalars, i.e., there are no scalar `sources.’ Pop quiz: what would change if the external scalars were replaced with localized sources and the diagrams had no external legs? Wiggly lines should be thought of as poorly drawn straight lines; i.e. there are no photons in the theory. Extra credit: what happens if this were scalar QED, and the wiggly lines were photon propagators? Shaded bubbles are also purely aesthetic, i.e. they are not 1PI graphs or anything fancy like that.

A caveat: I’ll include my guess for symmetry factors… I’m likely to be wrong! Any corrections (especially with explanations) would be appreciated and immortalized in the comments section. 🙂

Here we go:

Feynman stick figure (Flip says S=2)

Einstein stick figure, (Flip says S=3!)

`Cool’ Einstein stick figure, (Flip says S=3!*2*2)

`Feynman’s dog’ (see also this “Feynman’s dog” from a talk on mathematics an Futurama), (Flip says S=2 … but I’m not sure)

“Penguin” diagram (here’s some information about real penguin diagrams), the `eyes’ and shading are decorative and don’t contribute to the amplitude, (Flip says S=2)

Homage to Grant Wood’s American Gothic. (Flip guesses S=2^5.)