 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-307/3/iv/solution

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

V (ϕ) = ∣ W^{'} (ϕ) ∣^{2} = ∣ m ϕ + g ϕ^{2} ∣^{2} .

Explicitly,

V = m^{2} ∣ ϕ ∣^{2} + m (g ϕ + g^{*} ϕ^{*}) ∣ ϕ ∣^{2} + ∣ g ∣^{2} ∣ ϕ ∣^{4} .

The two supersymmetric vacua for

g \neq = 0

are

ϕ = 0

and

ϕ = - m / g

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