More on the Isomorphism SU(2)⊗SU(2)≅SO(4)
Abstract
In this paper we revisit the isomorphism
SU(2)⊗SU(2)≅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.