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

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.

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

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Cited by in corpus (5)

• From Symmetries to Commutant Algebras in Standard Hamiltonians
• Qudit quantum computation on matrix product states with global symmetry
• On ${\alpha }^{\prime }$-effects from $D$-branes in $4d\mathcal{N}=1$
• On the Magic Matrix by Makhlin and the B-C-H Formula in SO(4)
• Some properties of maximally entangled ELW game