A positive mass theorem for static causal fermion systems

Asymptotically flat static causal fermion systems are introduced. Their total mass is defined as a limit of surface layer integrals which compare the measures describing the asymptotically flat spacetime and a vacuum spacetime near spatial infinity. Our definition does not involve any regularity assumptions; it even applies to singular or generalized"quantum"spacetimes. A positive mass theorem is proven. Our methods and results explain why and how the causal action principle incorporates the nonlinear effects of gravity for static systems.