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Schwinger boson representation

Contracting two-mode oscillator bilinears with the Pauli matrices,

T^{a} = \frac{1}{2} σ_{ij}^{a} a_{i}^{†} a_{j},

gives

[T^{a}, T^{b}] = i ε_{ab c} T^{c}

. The subspace with total occupation

N

is the spin-

N /2

irreducible representation and has dimension

N + 1

.

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