A discrete variational principle in space-time

In the framework of the "principle of the fermionic projector" the following variational principle was proposed, \[ \sum_{x,y \in M} {\mathcal{L}}[P(x,y)\: P(y,x)] \;\rightarrow\; \min\:, \] 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.