Canonical Quantization of Scalar Fields — Mark Srednicki
Physics — QFT · path-integral-free-field-theory
Problem
Repeat the analysis of this section for the complex scalar field that was introduced in problem 3.5, and further studied in problem 5.1. Write your source term in the form J†φ+Jφ†, and find an explicit formula, analogous to eq. (8.10), for Z0(J†,J). Write down the appropriate generalization of eq. (8.14), and use it to compute ⟨0∣Tφ(x1)φ(x2)∣0⟩, ⟨0∣Tφ†(x1)φ(x2)∣0⟩, and ⟨0∣Tφ†(x1)φ†(x2)∣0⟩. Then verify your results by using the method of problem 8.4. Finally, give the appropriate generalization of eq. (8.17).