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

Kazuyuki Fujii·Hiroshi Oike·Tatsuo Suzuki
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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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Kazuyuki Fujii, Hiroshi Oike, Tatsuo Suzuki. 2007-01-12. More on the Isomorphism $SU(2)\otimes SU(2)\cong SO(4)$. https://doi.org/10.1142/s0219887807002120

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