# Feynman diagrams - swapped only by vertex label

Consider as an example $\phi^3$ theory, which contains at second order both the contractions: $$\newcommand{\mean}[1]{\langle #1 \rangle} \mean{\hat a_q \phi(\color{red}{x})}\mean{T\phi(x)\phi(x)}\mean{T\phi(y)\phi(y)}\mean{\phi(\color{red}{y})\hat a_p^\dagger}\tag1$$ $$\text{and}$$ $$\mean{\hat a_q \phi(\color{red}{y})}\mean{T\phi(x)\phi(x)}\mean{T\phi(y)\phi(y)}\mean{\phi(\color{red}{x})\hat a_p^\dagger}\tag2$$ (Important difference indicated in red). My question is: is it the convention to take these as separate diagrams or as the same (adjusting the symmetry factor accordingly)?

• If anyone knows how to do the Wick's contraction symbols in mathjax please could you let me know - I can't seem to find it anywhere. – Quantum spaghettification Aug 19 '17 at 5:13
• In your case, it would be acceptable to use LaTeX and CTAN simplewick, or Simple-Wick, to produce a PNG and include it in your question. – user154997 Aug 22 '17 at 7:10
• what are $a_q$ and $a_p^\dagger$? – AlQuemist Aug 22 '17 at 10:50
• @PhilosophiaeNaturalis They are by definition annihilation and creation operators of a particle into a state $\vec q$ and $\vec p$ respectively. – Quantum spaghettification Aug 22 '17 at 11:29
• What is then their relation to the field $\phi$? If $a_k$ and $\phi$ are independent, then $\langle a_k \phi \rangle = 0 = \langle a_k^\dagger \phi \rangle$. So, your question is not still clear enough to answer. Please provide your action. – AlQuemist Aug 22 '17 at 14:11