Hi, I'm currently going through Ticciati's book along with the notes from Sidney Coleman's course and I have a question pertaining to Wick diagrams/expansion of S.(adsbygoogle = window.adsbygoogle || []).push({});

In their example (section 4.3 of Ticciati and lecture 9 in Coleman's notes) they never seem to contract the adjoint nucleon field with itself nor the nucleon field with

itself; i.e., you only see contractions of [itex] \psi^\dagger (x_1)

[/itex] with [itex] \psi (x_2)[/itex] while you do see contractions of the meson field with itself, [itex] \phi(x_1) [/itex] contracted with [itex] \phi(x_2) [/itex]. Why is this so,

why not contract the adjoint nucleon field with itself, why not contract the nucleon field with itself? Also, what happens if you contract two appropriate fields at the

same spacetime point, e.g., [itex] \psi^\dagger (x_1) [/itex] contracted with [itex] \psi(x_1) [/itex]? It appears, from the formula for their contraction, that if you contract the two the resulting integral

should be

[tex]

\lim_{\epsilon \rightarrow 0}\int \frac{d^4 k}{(2\pi)^4} e^{-ik\cdot (x-x)}\frac{i}{k^2 - m^2 +i\epsilon} = \lim_{\epsilon \rightarrow 0}\int \frac{d^4 k}{(2\pi)^4} \frac{i}{k^2 - m^2 +i\epsilon}

[/tex]

which, I believe, is [itex] -1/2m [/itex]. Finally, does anyone know how to include the contraction symbols in latex? Thanks for your time.

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# Contracting operators in Wick diagrams

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