 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-301/4/a/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

L_{free} = - \frac{1}{4} F_{μν} F^{μν} + \partial_{μ} ϕ^{*} \partial^{μ} ϕ - m^{2} ϕ^{*} ϕ

and

L_{int} = i e A_{μ} (ϕ \partial^{μ} ϕ^{*} - ϕ^{*} \partial^{μ} ϕ) + e^{2} A_{μ} A^{μ} ϕ^{*} ϕ .

[A_{μ}] = [ϕ] = 1

and

[\partial_{μ}] = 1

, so

[e] = 0

. Both interactions have dimension four and

e

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