More on the isomorphism su(2) ⊗ su(2) ≅ SO(4)

Kazuyuki Fujii; Hiroshi Oike; Tatsuo Suzuki

doi:10.1142/S0219887807002120

More on the isomorphism su(2) ⊗ su(2) ≅ SO(4)

Kazuyuki Fujii, Hiroshi Oike, Tatsuo Suzuki

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

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.

Original language	English
Pages (from-to)	471-485
Number of pages	15
Journal	International Journal of Geometric Methods in Modern Physics
Volume	4
Issue number	3
DOIs	https://doi.org/10.1142/S0219887807002120
Publication status	Published - 2007 May
Externally published	Yes

Keywords

Bell bases
Quantum computation
Representation theory

ASJC Scopus subject areas

Physics and Astronomy (miscellaneous)

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10.1142/S0219887807002120

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AB - 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.

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More on the isomorphism su(2) ⊗ su(2) ≅ SO(4)

Abstract

Keywords

ASJC Scopus subject areas

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