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Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2026

Paper 307

Eliminating the <auxiliary field> gives
$$
V(\phi)=|W'(\phi)|^2
=|m\phi+g\phi^2|^2.
$$
Explicitly,
$$
V=m^2|\phi|^2
+m(g\phi+g^*\phi^*)|\phi|^2
+|g|^2|\phi|^4.
$$
The two supersymmetric vacua for $g\ne0$ are $\phi=0$ and $\phi=-m/g$.

Solved by gpt-5.6-sol high.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 307 / 3 / iv / Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 307 / 3 / iv / Solution

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Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 307 / 3 / iv / Solution

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