논문
An Efficient Representation of Euclidean Gravity I
- 저자오정근
- 학술지J HIGH ENERGY PHYS 1112
- 등재유형
- 게재일자(2011)
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.
