Symmetry factor of a general Feynman diagram

[omephy]

I am studying QFT from Srednicki's book. Let me ask a question about symmetry factor from this book.


Let, for specific values of $V$ and $P$ from eqn (9.11) we get some terms. One of them is a disconnected diagram consisted of two connected diagrams $C_1$ and $C_2$. The disconnected diagrams symmetry factor is, say, S; that is the term for disconnected diagram has a numerical coefficient: $\frac{1}{S}$. Now we write the term for disconnected diagram according to the eqn (9.12): $D = \frac{1}{S_D} \prod_I (C_I)^{n_I}$. In this case is this true: $S=\frac{1}{n_1 !} \times \frac{1}{n_2!} \times C_1$'s symmetry factor $\times C_2$'s symmetry factor? Here, $$S_D = \prod_I n_I !$$

 

[LightHero]

. Yes, this is true. The symmetry factor for the disconnected diagram D is equal to the product of the symmetry factors of each connected diagram C_1 and C_2, multiplied by the inverse of the product of the number of identical diagrams n_1 and n_2.