物质的几何模型
Geometric Models of Matter
摘要：
受孤立子模型的启发，我们提出了一种用具有自对偶Weyl张量的黎曼四维流形描述静态粒子的方法。对于带电粒子，四维流形是非紧的，并且在物理三维空间上渐近地被圆包围。这类似于卡鲁扎-克莱因对电磁学的描述，只不过我们交换了磁场和电场的作用，并且只假定在远离所讨论的粒子核的地方，渐近地存在束结构。我们用负的电荷和重子数分别确定了无穷远处圆丛的Chern类和4-流形的签名。电中性粒子用紧致4-流形来描述。我们通过研究陶布-努特流形作为电子的模型，阿蒂亚-希钦流形作为质子的模型，CP^2和Fubini-Study度规作为中子的模型，S^4和它的标准度规作为中微子的模型来说明我们的方法。
英文摘要：
Inspired by soliton models, we propose a description of static particles in terms of Riemannian 4-manifolds with self-dual Weyl tensor. For electrically charged particles, the 4-manifolds are non-compact and asymptotically fibred by circles over physical 3-space. This is akin to the Kaluza-Klein description of electromagnetism, except that we exchange the roles of magnetic and electric fields, and only assume the bundle structure asymptotically, away from the core of the particle in question. We identify the Chern class of the circle bundle at infinity with minus the electric charge and the signature of the 4-manifold with the baryon number. Electrically neutral particles are described by compact 4-manifolds. We illustrate our approach by studying the Taub-NUT manifold as a model for the electron, the Atiyah-Hitchin manifold as a model for the proton, CP^2 with the Fubini-Study metric as a model for the neutron, and S^4 with its standard metric as a model for the neutrino.
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。
