解构单极子和瞬子
Deconstructing Monopoles and Instantons
摘要：
利用等变映射构造了一个合适的全局投影子$p$，给出了2-球$S^2$上的Dirac瞬子、（2，2）-超球$S^{2,2}$上的分次瞬子和4-球$S^4$上的BPST瞬子的统一描述.这个投影器决定了相应向量丛的有限型截面的投影模。用正则联络$\nabla = p \circ d$计算拓扑荷，发现三种情况下拓扑荷均为-1。转置的投射器$q=p^t$给出电荷的值为+1;这表明投射器的转置，尽管在$K$ -理论中是同构，但不是恒等映射。我们还研究了在适当李群作用下的不变性。
英文摘要：
We give a unifying description of the Dirac monopole on the 2-sphere $S^2$, of a graded monopole on a (2,2)-supersphere $S^{2,2}$ and of the BPST instanton on the 4-sphere $S^4$, by constructing a suitable global projector $p$ via equivariant maps. This projector determines the projective module of finite type of sections of the corresponding vector bundle. The canonical connection $\nabla = p \circ d$ is used to compute the topological charge which is found to be equal to -1 for the three cases. The transposed projector $q=p^t$ gives the value +1 for the charges; this showing that transposition of projectors, although an isomorphism in $K$-theory, is not the identity map. We also study the invariance under the action of suitable Lie groups.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
