标题： 以行动驱动的流用于因果变分原理 显示英文标题

标题： Action-Driven Flows for Causal Variational Principles

摘要： 我们为因果变分原理引入了以行动驱动的流，这是一类源于基础物理应用的非凸变分问题。 在紧致情况下，通过使用最小化运动的方法构造了测度的霍尔德连续曲线。 如示例所示，由于作用量的非凸性，这些曲线通常不会有极限点。 这促使我们引入了一种新的惩罚项，以确保存在极限点，从而产生欧拉-拉格朗日方程的近似解。 这些方法和结果被适应并推广到有限维情况下的因果作用原理。 作为应用，我们在无限维情况下构造了因果费米子系统的测度流。 显示英文摘要

摘要： We introduce action-driven flows for causal variational principles, being a class of non-convex variational problems emanating from applications in fundamental physics. In the compact setting, H\"older continuous curves of measures are constructed by using the method of minimizing movements. As is illustrated in examples, these curves will in general not have a limit point, due to the non-convexity of the action. This leads us to introducing a novel penalization which ensures the existence of a limit point, giving rise to approximate solutions of the Euler-Lagrange equations. The methods and results are adapted and generalized to the causal action principle in the finite-dimensional case. As an application, we construct a flow of measures for causal fermion systems in the infinite-dimensional situation.