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QFT — Michael Luke Lectures · Problem V.2
Interacting Fields — Michael Luke
Physics — QFT · nucleon-field-matrix-elements
Problem From the explicit expansion of ψ \psi ψ in terms of b † ( k ) b^\dagger(k) b † ( k ) and c ( k ) c(k) c ( k ) and Eq. (V.75), show that
⟨ 0 ∣ ψ ( x 1 ) ψ ( x 2 ) ∣ p 1 ; p 2 ⟩ = e − i p 1 ⋅ x 1 − i p 2 ⋅ x 2 + e − i p 1 ⋅ x 2 − i p 2 ⋅ x 1 . (V.79) \langle 0 | \psi(x_1)\psi(x_2) | p_1; p_2 \rangle = e^{-ip_1 \cdot x_1 - ip_2 \cdot x_2} + e^{-ip_1 \cdot x_2 - ip_2 \cdot x_1}. \tag{V.79} ⟨ 0∣ ψ ( x 1 ) ψ ( x 2 ) ∣ p 1 ; p 2 ⟩ = e − i p 1 ⋅ x 1 − i p 2 ⋅ x 2 + e − i p 1 ⋅ x 2 − i p 2 ⋅ x 1 . ( V.79 )
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