The perturbation theory for critical points of causal variational principles is developed. We first analyze the class of perturbations obtained by multiplying the universal measure by a weight function and taking the push-forward under a dif- feomorphism. Then the constructions are extended to convex combinations of such measures, leading to perturbation expansions for the mean and the fluctuation of the measure, both being coupled in higher order perturbation theory. It is explained how our methods and results apply to the causal action principle for causal fermion systems. It is shown how the perturbation expansion in the continuum limit and the effect of microscopic mixing are recovered in specific limiting cases.

中文翻译：

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因果变分原理临界点的微扰理论

发展了因果变分原理临界点的微扰理论。我们首先分析通过将通用测度乘以权重函数并在微分同胚下进行前推而获得的扰动类别。然后将构造扩展到这些度量的凸组合，导致均值和度量波动的扰动扩展，两者都在高阶扰动理论中耦合。解释了我们的方法和结果如何应用于因果费米子系统的因果作用原理。显示了在特定极限情况下如何恢复连续介质极限中的扰动扩展和微观混合的影响。