Magnetic translation algebra

For constant

B

,

T_{r} T_{r^{'}} = exp (\frac{i e}{ℏ} (r \times r^{'}) \cdot B) T_{r^{'}} T_{r} .

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- Magnetic flux quantum Magnetic translation algebra

Magnetic flux quantum

Magnetic translations along two lattice vectors commute when their cell flux obeys

\frac{e Φ}{ℏ} \in 2 π Z, equivalently Φ \in \frac{h}{e} Z .

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Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 4 / 34B / c / Solution

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