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arXiv quant-ph/02060052002-06-02quant-phhep-thmath-phmath.MP

SU(N) Coherent States

Manu Mathur, H. S. Mani

备注：: 25 pages, LaTex, no figures
发表信息：: J.Math.Phys. 43 (2002) 5351
DOI：: 10.1063/1.1513651

英文摘要：

We generalize Schwinger boson representation of SU(2) algebra to SU(N) and define coherent states of SU(N) using $2(2^{N-1}-1)$ bosonic harmonic oscillator creation and annihilation operators. We give an explicit construction of all (N-1) Casimirs of SU(N) in terms of these creation and annihilation operators. The SU(N) coherent states belonging to any irreducible representations of SU(N) are labelled by the eigenvalues of the Casimir operators and are characterized by (N-1) complex orthonormal vectors describing the SU(N) manifold. The coherent states provide a resolution of identity, satisfy the continuity property, and possess a variety of group theoretic properties.

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