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More on the Isomorphism $SU(2)\otimes SU(2)\cong SO(4)$

Quantum Physics 2008-11-26 v2 High Energy Physics - Theory Mathematical Physics math.MP

Abstract

In this paper we revisit the isomorphism SU(2)SU(2)SO(4)SU(2)\otimes SU(2)\cong SO(4) to apply to some subjects in Quantum Computation and Mathematical Physics. The unitary matrix QQ 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)SU(2n)/SO(2n) which characterizes entanglements in the case of n=2n=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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Cite

@article{arxiv.quant-ph/0608186,
  title  = {More on the Isomorphism $SU(2)\otimes SU(2)\cong SO(4)$},
  author = {Kazuyuki Fujii and Hiroshi Oike and Tatsuo Suzuki},
  journal= {arXiv preprint arXiv:quant-ph/0608186},
  year   = {2008}
}

Comments

Latex ; 19 pages ; 5 figures ; minor changes. To appear in International Journal of Geometric Methods in Modern Physics (vol.4, no.3)