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- Use Wick's theorem to reduce the following time ordered product to a sum of normal products. \[T\big(:\bar{\psi}(x) \gamma_5\psi(x) \phi(x):\ :\bar{\psi}(y)\gamma_5\psi(y) \phi(y):\big)\] where \(\psi(x),\phi(x)\) represent spin half(nucleon) and spin zero (pion) fields respectively.
- Identify terms that will contribute to pion nucleon scattering.
- Find term(s),if any, that will contribute to pion pion scattering?Are there terms which contribute to nucleon anti nucleon annihilation into two pions? Identify these terms?
- Draw position space Feynman diagrams for the processes mentioned in parts (b) and (c).
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