The Theory of Causal Fermion Systems

The causal action principle or, more generally, causal variational principles give rise to flows of measures such that the action decreases along the flow lines. In the smooth setting, this is similar to a gradient flow, where the measure flows in the “direction of steepest descent.” In the general non-smooth situation, the flow is constructed in [FG25] using the method of minimizing movements. This method makes it possible to construct approximate solutions of the Euler-Lagrange equations even in the infinite-dimensional case.