A discrete variational principle in space-time

In the framework of the "principle of the fermionic projector" the following variational principle was proposed, $$\sum _{x,y\in M}\mathcal{L}[P(x,y)P(y,x)]\to min,$$ where the "Langrangian" $\mathcal{L}$ is given by $$\mathcal{L}[A]=|A{|}^2-\mu |A^2|.$$ Here~$P$ is the fermionic projector, $M$ denotes the points of discrete space-time, $\mu$ is a Lagrangian multiplier and~$|.|$ is the so-called spectral weight. The purpose of the talk is to motivate this variational principle and to explain some analytical aspects. In particular, I want to work out in which sense the vacuum is a stable minimizer of this variational principle. The talk is intended for analysts, no knowledge about mathematical physics is required.