dorsal/arxiv
View SchemaPhase Space Reduction for Star-Products: An Explicit Construction for CP^n
| Authors | M. Bordemann, M. Brischle, C. Emmrich, S. Waldmann |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9503004 |
| URL | https://arxiv.org/abs/q-alg/9503004 |
| DOI | 10.1007/BF00714403 |
Abstract
We derive a closed formula for a star-product on complex projective space and on the domain $SU(n+1)/S(U(1)\times U(n))$ using a completely elementary construction: Starting from the standard star-product of Wick type on $C^{n+1} \setminus \{ 0 \}$ and performing a quantum analogue of Marsden-Weinstein reduction, we can give an easy algebraic description of this star-product. Moreover, going over to a modified star-product on $C^{n+1} \setminus \{ 0 \}$, obtained by an equivalence transformation, this description can be even further simplified, allowing the explicit computation of a closed formula for the star-product on $\CP^n$ which can easily transferred to the domain $SU(n+1)/S(U(1)\times U(n))$.
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"date_created": "2026-03-02T18:01:24.714000Z",
"date_modified": "2026-03-02T18:01:24.714000Z",
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"abstract": "We derive a closed formula for a star-product on complex projective space and\non the domain $SU(n+1)/S(U(1)\\times U(n))$ using a completely elementary\nconstruction: Starting from the standard star-product of Wick type on $C^{n+1}\n\\setminus \\{ 0 \\}$ and performing a quantum analogue of Marsden-Weinstein\nreduction, we can give an easy algebraic description of this star-product.\nMoreover, going over to a modified star-product on $C^{n+1} \\setminus \\{ 0 \\}$,\nobtained by an equivalence transformation, this description can be even further\nsimplified, allowing the explicit computation of a closed formula for the\nstar-product on $\\CP^n$ which can easily transferred to the domain\n$SU(n+1)/S(U(1)\\times U(n))$.",
"arxiv_id": "q-alg/9503004",
"authors": [
"M. Bordemann",
"M. Brischle",
"C. Emmrich",
"S. Waldmann"
],
"categories": [
"q-alg",
"dg-ga",
"hep-th",
"math.DG",
"math.QA"
],
"doi": "10.1007/BF00714403",
"title": "Phase Space Reduction for Star-Products: An Explicit Construction for CP^n",
"url": "https://arxiv.org/abs/q-alg/9503004"
},
"schema_id": "dorsal/arxiv",
"source": {
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"variant": "snapshot-2026-03-01",
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