dorsal/arxiv
View SchemaMore on the Isomorphism $SU(2)\otimes SU(2)\cong SO(4)$
| Authors | Kazuyuki Fujii, Hiroshi Oike, Tatsuo Suzuki |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0608186 |
| URL | https://arxiv.org/abs/quant-ph/0608186 |
| DOI | 10.1142/S0219887807002120 |
| Journal | Int.J.Geom.Meth.Mod.Phys.4:471-485,2007 |
Abstract
In this paper we revisit the isomorphism $SU(2)\otimes SU(2)\cong SO(4)$ to apply to some subjects in Quantum Computation and Mathematical Physics. The unitary matrix $Q$ by Makhlin giving the isomorphism as an adjoint action is studied and generalized from a different point of view. Some problems are also presented. In particular, the homogeneous manifold $SU(2n)/SO(2n)$ which characterizes entanglements in the case of $n=2$ is studied, and a clear-cut calculation of the universal Yang-Mills action in (hep-th/0602204) is given for the abelian case.
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"abstract": "In this paper we revisit the isomorphism $SU(2)\\otimes SU(2)\\cong SO(4)$ to\napply to some subjects in Quantum Computation and Mathematical Physics.\n The unitary matrix $Q$ by Makhlin giving the isomorphism as an adjoint action\nis studied and generalized from a different point of view. Some problems are\nalso presented.\n In particular, the homogeneous manifold $SU(2n)/SO(2n)$ which characterizes\nentanglements in the case of $n=2$ is studied, and a clear-cut calculation of\nthe universal Yang-Mills action in (hep-th/0602204) is given for the abelian\ncase.",
"arxiv_id": "quant-ph/0608186",
"authors": [
"Kazuyuki Fujii",
"Hiroshi Oike",
"Tatsuo Suzuki"
],
"categories": [
"quant-ph",
"hep-th",
"math-ph",
"math.MP"
],
"doi": "10.1142/S0219887807002120",
"journal_ref": "Int.J.Geom.Meth.Mod.Phys.4:471-485,2007",
"title": "More on the Isomorphism $SU(2)\\otimes SU(2)\\cong SO(4)$",
"url": "https://arxiv.org/abs/quant-ph/0608186"
},
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