Papers
An Efficient Representation of Euclidean Gravity I
- Author오정근
- JournalJ HIGH ENERGY PHYS 1112 (2011
- Classification of papersSCI
We explore how the topology of spacetime fabric is encoded into the local structure of Riemannian metrics using
the gauge theory formulation of Euclidean gravity. In part I, we provide a rigorous mathematical foundation to
prove that a general Einstein manifold arises as the sum of SU(2)_L Yang-Mills instantons and SU(2)_R anti-
instantons where SU(2)_L and SU(2)_R are normal subgroups of the four-dimensional Lorentz group Spin(4) =
SU(2)_L x SU(2)_R. Our proof relies only on the general properties in four dimensions: The Lorentz group
Spin(4) is isomorphic to SU(2)_L x SU(2)_R and the six-dimensional vector space of two-forms splits canonically
into the sum of three-dimensional vector spaces of self-dual and anti-self-dual two-forms. Consolidating these
two, it turns out that the splitting of Spin(4) is deeply correlated with the decomposition of two-forms on four-
manifold which occupies a central position in the theory of four-manifolds.
the gauge theory formulation of Euclidean gravity. In part I, we provide a rigorous mathematical foundation to
prove that a general Einstein manifold arises as the sum of SU(2)_L Yang-Mills instantons and SU(2)_R anti-
instantons where SU(2)_L and SU(2)_R are normal subgroups of the four-dimensional Lorentz group Spin(4) =
SU(2)_L x SU(2)_R. Our proof relies only on the general properties in four dimensions: The Lorentz group
Spin(4) is isomorphic to SU(2)_L x SU(2)_R and the six-dimensional vector space of two-forms splits canonically
into the sum of three-dimensional vector spaces of self-dual and anti-self-dual two-forms. Consolidating these
two, it turns out that the splitting of Spin(4) is deeply correlated with the decomposition of two-forms on four-
manifold which occupies a central position in the theory of four-manifolds.
We explore how the topology of spacetime fabric is encoded into the local structure of Riemannian metrics using
the gauge theory formulation of Euclidean gravity. In part I, we provide a rigorous mathematical foundation to
prove that a general Einstein manifold arises as the sum of SU(2)_L Yang-Mills instantons and SU(2)_R anti-
instantons where SU(2)_L and SU(2)_R are normal subgroups of the four-dimensional Lorentz group Spin(4) =
SU(2)_L x SU(2)_R. Our proof relies only on the general properties in four dimensions: The Lorentz group
Spin(4) is isomorphic to SU(2)_L x SU(2)_R and the six-dimensional vector space of two-forms splits canonically
into the sum of three-dimensional vector spaces of self-dual and anti-self-dual two-forms. Consolidating these
two, it turns out that the splitting of Spin(4) is deeply correlated with the decomposition of two-forms on four-
manifold which occupies a central position in the theory of four-manifolds.
the gauge theory formulation of Euclidean gravity. In part I, we provide a rigorous mathematical foundation to
prove that a general Einstein manifold arises as the sum of SU(2)_L Yang-Mills instantons and SU(2)_R anti-
instantons where SU(2)_L and SU(2)_R are normal subgroups of the four-dimensional Lorentz group Spin(4) =
SU(2)_L x SU(2)_R. Our proof relies only on the general properties in four dimensions: The Lorentz group
Spin(4) is isomorphic to SU(2)_L x SU(2)_R and the six-dimensional vector space of two-forms splits canonically
into the sum of three-dimensional vector spaces of self-dual and anti-self-dual two-forms. Consolidating these
two, it turns out that the splitting of Spin(4) is deeply correlated with the decomposition of two-forms on four-
manifold which occupies a central position in the theory of four-manifolds.