To appear in Int. J. Mod. Phys. A Previous title: An outlook on quantum gravity from an algebraic perspective. 39 pages, 1 xy-pic figure, LaTex Reasons for new version: added references, change of title and some comments more up-to-date
The first part is an introductory description of a small cross-section of the literature on algebraic methods in non-perturbative quantum gravity with a specific focus on viewing algebra as a laboratory in which to deepen understanding of the nature of geometry. This helps to set the context for the second part, in which we describe a new algebraic characterisation of the Dirac operator in non-commutative geometry and then use it in a calculation on the form of the fermion mass matrix. Assimilating and building on the various ideas described in the first part, the final part consists of an outline of a speculative perspective on (non-commutative) quantum spectral gravity. This is the second of a pair of papers so far on this project.
Fermion masses, mass-mixing and the almost commutative geometry of the Standard Model
我们研究标准模型在当前实验测量的准确度范围内是否满足Dabrowski，D'Andrea，Sitarz，Lett Math Phys（2018）108：1323中介绍和研究的Hodge对偶条件。我们证明了中微子和夸克的质量混合以及费米子质量的差异是这一性质的必要条件。我们证明，目前的数据支持新的几何特征的标准模型，霍奇对偶，提供所有的中微子是大质量的。
Causal Fermion Systems, Non-Commutative Geometry and Generalized Trace Dynamics
Universität Regensburg（雷根斯堡大学）；Max-Planck Institute for Gravitational Physics（马克斯·普朗克引力物理研究所）；Inter-University Centre for Astronomy and Astrophysics（大学间天体物理中心）；Tata Institute of Fundamental Research（塔塔基础研究所）
