We review recent results obtained by using the spectral action applied to some simple physical models built in the noncommutative geometry framework. The first result, based on the generalization of the spectral action principle to the case of the fermionic action leads to the lowest order corrections that can possibly explain the huge difference between the electron and neutrino masses. In the second case, the extension of the family of Dirac operators for the product of finite geometry with the Riemannian manifold but without a product metric leads to a theory with two metrics that is similar to the models of bimetric gravity.

中文翻译：

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通过光谱作用走向新物理学的迹象

我们回顾了通过使用应用于非对易几何框架中构建的一些简单物理模型的光谱作用获得的最新结果。第一个结果基于将光谱作用原理推广到费米子作用的情况，导致最低阶校正，这可能解释电子和中微子质量之间的巨大差异。在第二种情况下，将狄拉克算子家族扩展为具有黎曼流形但没有乘积度量的有限几何乘积，导致了一个具有两个度量的理论，类似于双度量引力模型。