Topological aspects of Yang-Mills theory
Topological aspects of Yang-Mills theory
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杨-米尔斯理论的拓扑方面
DOI：
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发表时间：
1978
期刊：
影响因子：
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通讯作者：
J. D. Jones
中科院分区：
文献类型：
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作者：
M. Atiyah;J. D. Jones
mapsS3→G的空间具有给出群G的杨-米尔斯理论拓扑量子数的分量。空间的每个分量都有进一步的拓扑不变量。当eng =SU(2)时，我们证明这些不变量（同调群）被瞬子空间“捕获”。利用这些不变量，我们证明了无质量狄拉克方程（在欧几里得4空间中）具有任意多个独立解（对于固定的瞬数）的势必须存在。
The space of mapsS3 →G has components which give the topological quantum number of Yang-Mills theory for the groupG. Each component of the space has further topological invariants. WhenG=SU(2) we show that these invariants (the homology groups) are “captured” by the space of instantons. Using these invariants we show that potentials must exist for which the massless Dirac equation (in Euclidean 4-space) has arbitrarily many independent solutions (for fixed instanton number).