dorsal/arxiv
View SchemaSU(N) Coherent States
| Authors | Manu Mathur, H. S. Mani |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0206005 |
| URL | https://arxiv.org/abs/quant-ph/0206005 |
| DOI | 10.1063/1.1513651 |
| Journal | J.Math.Phys. 43 (2002) 5351 |
Abstract
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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"abstract": "We generalize Schwinger boson representation of SU(2) algebra to SU(N) and\ndefine coherent states of SU(N) using $2(2^{N-1}-1)$ bosonic harmonic\noscillator creation and annihilation operators. We give an explicit\nconstruction of all (N-1) Casimirs of SU(N) in terms of these creation and\nannihilation operators. The SU(N) coherent states belonging to any irreducible\nrepresentations of SU(N) are labelled by the eigenvalues of the Casimir\noperators and are characterized by (N-1) complex orthonormal vectors describing\nthe SU(N) manifold. The coherent states provide a resolution of identity,\nsatisfy the continuity property, and possess a variety of group theoretic\nproperties.",
"arxiv_id": "quant-ph/0206005",
"authors": [
"Manu Mathur",
"H. S. Mani"
],
"categories": [
"quant-ph",
"hep-th",
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"math.MP"
],
"doi": "10.1063/1.1513651",
"journal_ref": "J.Math.Phys. 43 (2002) 5351",
"title": "SU(N) Coherent States",
"url": "https://arxiv.org/abs/quant-ph/0206005"
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