挠率空间中的瞬子与手征反常

Instantons and chiral anomaly in space with torsion

空间的拓扑性质对该空间负载的物理场有极其重要的影响.对挠率不为零的空间,可用规范势分解方法探讨其拓扑性质与其上负载的Higgs场之间的关系.结果表明,表征Higgs场瞬子的各环绕数的和取决于挠率空间的拓扑性质,且随着空间拓扑性质的改变,瞬子会产生或湮灭.此外,挠率空间中的手征反常只在具有对称相的Higgs场和标量纤维场中出现.规范势分解方法的结果比经典的多瞬子解更加精确,因而能更细致地描述物理场和负载它的空间之间的联系.

The topological properties of a space have important influence on the physical field this space carries on. In a space with torsion, the method of gauge potential decomposition can be used to discuss the relationship between this space and the Higgs field it carries on. The results indicate that the sum of winding numbers which characterize intantons depends on the topological properties of space with torsion. When the properties of space changes, intantons will emerge or vanish. Furthermore, the chiral anomaly only exists in the symmetrical phase of Higgs field and scalar vierbein field. The method of gauge potential decomposition is more accurate than the classical multi-intanton solution; therefore, it can describe the relationship between the physical field and its space more precisely.