 Oscillator bilinear commutator

ID: oscillator-bilinear-commutator

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

For bosonic modes satisfying

[a_{i}, a_{j}^{†}] = δ_{ij}

, the number-preserving bilinears

T_{ij} = a_{i}^{†} a_{j}

obey

[T_{ij}, T_{k l}] = δ_{jk} T_{i l} - δ_{i l} T_{kj} .

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