Symmetry factors for feynman diagrams

Jessica_S

Hello

I have to calculate symmetry factors for the following feynman diagrams for my qft class, and would be hugely grateful if anyone could point out any mistakes (I'm sure there are lots!) that I've made.

The diagrams!

And here are my answers:

(a) Symmetry factor, S = 2^3 = 8. Interchange of 2 pairs of equivalent lines and swapping the ends of the bubble line

(b) S = 2^7 = 128. Swapping 5 pairs of equivalent lines, 2 pairs of equivalent vertices.

(c) S = 2 x 4! = 48. Swapping the two vertices, and interchanging the 4 internal lines.

(d) S = 2^4 = 16. Swapping the two internal lines, interchanging the ends of the two bubbles, interchanging the two vertices.

(e) S = 2^3 = 8. Swapping the two vertices attached to the external lines, interchanging the ends of the bubble, swapping the lines on the top of the bigger loop.

(f) This one has me very confused...

(g) S = 2^6 = 64. Exchanging 4 pairs of equivalent lines, swapping one pair of equivalent vertices, interchanging the ends of the bubble.

Avodyne

You're overcounting in several cases. Swapping external lines does not count (think of them as being labeled). Similarly, swapping vertices that have external lines attached does not count. Also, sometimes a vertex swap is equivalent to a line swap, and so does not count twice.

And sometimes the symmetry factor is 1 ...

Jessica_S

Cool thank you - that answers a few things I was wondering about.