Dirac operators on the Taub-NUT space, monopoles and SU(2) representations
Dirac operators on the Taub-NUT space, monopoles and SU(2) representations
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DOI：
10.1007/jhep01(2014)114
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发表时间：
2014-01-22
影响因子：
5.4
通讯作者：
Schroers, Bernd J.
中科院分区：
文献类型：
--
作者：
Jante, Rogelio;Schroers, Bernd J.
我们分析了耦合到具有自对偶曲率的阿贝尔规范场的Taub-NUT流形上的Dirac算子的可规范化零模，并将其解释为耦合到Dirac规范场的2-球面上的Dirac算子的零模.我们表明，零模空间分解成一个直接的总和不可约SU（2）表示的所有维度的限制所确定的旋量收费相对于阿贝尔规范群。我们的分解提供了一个解释的指数公式，由于教皇，并提供了一个可能的模型自旋在最近提出的几何模型的问题。
We analyse the normalisable zero-modes of the Dirac operator on the Taub-NUT manifold coupled to an abelian gauge field with self-dual curvature, and interpret them in terms of the zero modes of the Dirac operator on the 2-sphere coupled to a Dirac monopole. We show that the space of zero modes decomposes into a direct sum of irreducible SU(2) representations of all dimensions up to a bound determined by the spinor charge with respect to the abelian gauge group. Our decomposition provides an interpretation of an index formula due to Pope and provides a possible model for spin in recently proposed geometric models of matter.