Geometric models of matter
Geometric models of matter
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DOI：
10.1098/rspa.2011.0616
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发表时间：
2012-05-08
影响因子：
3.5
通讯作者：
Schroers, B. J.
中科院分区：
文献类型：
--
作者：
Atiyah, M. F.;Manton, N. S.;Schroers, B. J.
受孤子模型的启发，我们提出用具有自对偶 Weyl 张量的黎曼 4 流形来描述静态粒子。对于带电粒子，4 流形是非紧致的，并且由物理 3 空间上的圆渐近纤维化。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角色，并且仅渐近地假设束结构，远离所讨论的粒子的核心。我们用负电荷确定了无穷远圆束的陈氏类，并且至少暂时用重子数确定了 4 流形的签名。电中性粒子由紧凑的 4 流形描述。我们通过研究 Taub-Newman、Unti、Tamburino (Taub-NUT) 流形作为电子模型、Atiyah-Hitchin 流形作为质子模型、使用 Fubini-Study 度量的 CP2 作为中子模型以及使用其标准度量的 S-4 作为中微子模型来说明我们的方法。
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, at least provisionally, 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-Newman, Unti, Tamburino (Taub-NUT) manifold as a model for the electron, the Atiyah-Hitchin manifold as a model for the proton, CP2 with the Fubini-Study metric as a model for the neutron and S-4 with its standard metric as a model for the neutrino.