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- W3197290413 abstract "Einstein manifolds in four dimensions are composed of $SU(2)_+$ Yang-Mills instantons and $SU(2)_-$ anti-instantons. This fact is based on the fundamental theorems that the four-dimensional Lorentz group $SO(4)$ is a direct product of two groups $SU(2)_pm$ and the vector space of two-forms decomposes into the space of self-dual and anti-self-dual two-forms. A central point is that the splitting of the Lie algebra $so(4) cong su(2)_+ oplus su(2)_-$ is isomorphic to the decomposition of the two-form vector space. We now consider whether such an inevitable division of four-dimensional Einstein manifolds can be unified into a five-dimensional Einstein manifold. This unification scheme of four-manifolds is similar to the grand unification of Standard Model since the product group $SO(4) cong SU(2)_+ otimes SU(2)_-/mathbb{Z}_2$ must be embedded into the simple group $SO(5) = Sp(2)/mathbb{Z}_2$. Our group-theoretic approach reveals the anatomy of Riemannian manifolds quite similar to the quark model of hadrons in which two independent Yang-Mills instantons represent a substructure of Einstein manifolds." @default.
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- W3197290413 date "2021-08-31" @default.
- W3197290413 modified "2023-10-01" @default.
- W3197290413 title "Unification of Einstein Manifolds" @default.
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