 Solution

ID: past-exam-of-the-theoretical-physics-major-option-course-of-the-university-of-oxford/2022/6/b/solution

Put

V (ϕ) = m^{2} ϕ^{2} /2 + \sum_{n > 2} λ_{n} ϕ^{n} / n!

□ ϕ + V^{'} (ϕ) = 0

, or explicitly

(□ + m^{2}) ϕ + n > 2 \sum \frac{λ _{n}}{( n - 1 )!} ϕ^{n - 1} = 0.

ϕ^{n} / n!

ϕ^{n - 1} / (n - 1)!

; all interaction terms therefore enter with the displayed plus sign for the chosen Minkowski metric.

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