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Interacting Fields — Michael Luke
Physics — QFT · wick-theorem-scattering-processes
Problem Consider the term in the Wick expansion
( − i g ) 2 2 ! ∫ d 4 x 1 ∫ d 4 x 2 : ψ † ( x 1 ) ψ ( x 1 ) ϕ ( x 1 ) ψ † ( x 2 ) ‾ ψ ( x 2 ) ϕ ( x 2 ) : (V.67) \frac{(-ig)^2}{2!} \int d^4x_1 \int d^4x_2 :\psi^\dagger(x_1)\overline{\psi(x_1)\phi(x_1)\psi^\dagger(x_2)}\psi(x_2)\phi(x_2): \tag{V.67} 2 ! ( − i g ) 2 ∫ d 4 x 1 ∫ d 4 x 2 : ψ † ( x 1 ) ψ ( x 1 ) ϕ ( x 1 ) ψ † ( x 2 ) ψ ( x 2 ) ϕ ( x 2 ) : ( V.67 ) 2 → 2 2 \to 2 2 → 2 N + ϕ → N + ϕ , N ‾ + ϕ → N ‾ + ϕ , N + N ‾ → ϕ + ϕ , ϕ + ϕ → N + N ‾ . N + \phi \to N + \phi, \quad \overline{N} + \phi \to \overline{N} + \phi, \quad N + \overline{N} \to \phi + \phi, \quad \phi + \phi \to N + \overline{N}. N + ϕ → N + ϕ , N + ϕ → N + ϕ , N + N → ϕ + ϕ , ϕ + ϕ → N + N . Browse the problem library