The bundle of the 2-forms on 6-manifold decomposes into three subbundles such that Λ~2(R^6) = Λ~2_1⊕Λ~2_6⊕Λ~2_8 with dimensions 1,6 and 8,respectively.The self and anti self duality solutions of the 2-forms,call...The bundle of the 2-forms on 6-manifold decomposes into three subbundles such that Λ~2(R^6) = Λ~2_1⊕Λ~2_6⊕Λ~2_8 with dimensions 1,6 and 8,respectively.The self and anti self duality solutions of the 2-forms,called Φ-duality,are handled and these solutions show that the anti self dual gauge fields live on the subbundles Λ~2_1 and Λ~2_6 while the self ones equations on Λ28.Also the solution on Λ~2_1 presents a flat connection.In addition,the curvatures of the connections on Λ~2_6 and Λ~2_8 have Tr[F^3] = 0,and so the topological invariants determined by the Chern classes,i.e.topological charge,consist only on the second Chern class.In the result of this case,the anti self and self Φ-dual gauge invariant Lagrangians of defined on both subbundles are bounded by the same topological charge.Also,one gives a quantization case to be relating to the instanton number.展开更多
The self-duality concept for the Higgs field is handled in the presence of contact geometry in 5 dimensions. A non-trivial SO（3） Higgs field lives only on the fifth dimension of the contact manifold because of the c...The self-duality concept for the Higgs field is handled in the presence of contact geometry in 5 dimensions. A non-trivial SO（3） Higgs field lives only on the fifth dimension of the contact manifold because of the contact structure, while the SD Yang-Mills field lives in the 4-dimensional hyperplane of the contact manifold. The Higgs and SD Yang-Mills fields do not interact with one another.展开更多
文摘The bundle of the 2-forms on 6-manifold decomposes into three subbundles such that Λ~2(R^6) = Λ~2_1⊕Λ~2_6⊕Λ~2_8 with dimensions 1,6 and 8,respectively.The self and anti self duality solutions of the 2-forms,called Φ-duality,are handled and these solutions show that the anti self dual gauge fields live on the subbundles Λ~2_1 and Λ~2_6 while the self ones equations on Λ28.Also the solution on Λ~2_1 presents a flat connection.In addition,the curvatures of the connections on Λ~2_6 and Λ~2_8 have Tr[F^3] = 0,and so the topological invariants determined by the Chern classes,i.e.topological charge,consist only on the second Chern class.In the result of this case,the anti self and self Φ-dual gauge invariant Lagrangians of defined on both subbundles are bounded by the same topological charge.Also,one gives a quantization case to be relating to the instanton number.
文摘The self-duality concept for the Higgs field is handled in the presence of contact geometry in 5 dimensions. A non-trivial SO（3） Higgs field lives only on the fifth dimension of the contact manifold because of the contact structure, while the SD Yang-Mills field lives in the 4-dimensional hyperplane of the contact manifold. The Higgs and SD Yang-Mills fields do not interact with one another.
