Causal fermion systems incorporate local gauge symmetry in the sense that the Lagrangian and all inherent structures are invariant under local phase transformations of the physical wave functions. In the present paper, it is explained and worked out in detail that, despite this local gauge freedom, the structures of a causal fermion system give rise to distinguished gauges where the local gauge freedom is fixed completely up to global gauge transformations. The main method is to use spectral and polar decompositions of operators on Hilbert spaces and on indefinite inner product spaces. We also introduce and make use of a Riemannian metric, which is induced on the manifold of all regular correlation operators by the Hilbert–Schmidt scalar product. Gaussian coordinate systems corresponding to this Riemannian metric are constructed. Moreover, we work with so-called wave charts where the physical wave functions are used as coordinates. Our constructions and results are illustrated in the example of Dirac sea configurations in finite and infinite spatial volume.

中文翻译：

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因果费米子系统的规范固定程序

因果费米子系统结合了局部规范对称性，即拉格朗日函数和所有固有结构在物理波函数的局部相变下是不变的。在本文中，详细解释和计算出，尽管有这种局部规范自由，因果费米子系统的结构产生了不同的规范，其中局部规范自由完全固定到全局规范转换。主要方法是在 Hilbert 空间和不定内积空间上使用算子的谱分解和极坐标分解。我们还引入并使用了黎曼度量，它是由希尔伯特-施密特标量积在所有正则相关算子的流形上导出的。构建了对应于该黎曼度量的高斯坐标系。而且，我们使用所谓的波图，其中物理波函数用作坐标。我们的构造和结果在有限和无限空间体积中的狄拉克海配置示例中进行了说明。