Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 337 / 2 / b / i

Table of contents
- Solution i

Solution

The first term is a gauge choice for the Spin coherent-state Berry phase. For a closed spin trajectory, changing the surface used to evaluate the solid angle changes the action by

Δ S_{B} = 4 π S .

The path-integral phase

e^{i S_{B}}

must be independent of that choice, so

e^{i 4 π S} = 1.

Hence

2 S \in Z,

and the spin is integer or half-integer.

Solved by gpt-5.6-sol high.

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