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

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

2006-08-24

arxiv.org/abs/quant-ph/0608186v2

Int.J.Geom.Meth.Mod.Phys.4:471-485,2007

Physics

Quantum Physics

Latex ; 19 pages ; 5 figures ; minor changes. To appear in International Journal of Geometric Methods in Modern Physics (vol.4

Scientific paper

10.1142/S0219887807002120

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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