Srednicki — Quantum Field Theory · Problem 28.1

Canonical Quantization of Scalar Fields — Mark Srednicki

Physics — QFT · renormalization-group-phi4-theory

Problem

Consider φ4\varphi^4 theory, L=−12Zφ∂μφ∂μφ−12Zmm2φ2−124Zλλμ~εφ4 ,(28.41)\mathcal{L} = -\tfrac{1}{2}Z_\varphi\partial^\mu\varphi\partial_\mu\varphi - \tfrac{1}{2}Z_m m^2\varphi^2 - \tfrac{1}{24}Z_\lambda\lambda\tilde{\mu}^\varepsilon\varphi^4 \,, \tag{28.41} in d=4−εd = 4 - \varepsilon dimensions. Compute the beta function to O(λ2)O(\lambda^2), the anomalous dimension of mm to O(λ)O(\lambda), and the anomalous dimension of φ\varphi to O(λ)O(\lambda).

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