We quantize the interaction of gravity with Yang-Mills and spinor fields, hence offering a quantum theory incorporating all four fundamental forces of nature. Using canonical quantization we obtain solutions of the Wheeler-DeWitt equation in a vector bundle and the method of second quantization leads to a symplectic vector space $(V,\omega)$ and a corresponding CCR representation for the bosonic components and a CAR relation for the fermionic part. The solution space of the Wheeler-DeWitt equation is invariant under gauge transformations and under isometries in the spacelike base space $\mathcal S_0$ of a given Riemannian metric $\rho_{ij}$. We also define a net of local subalgebras which satisfy four of the Haag-Kastler axioms.

We present some old and new results on the problem of deriving Plateau's laws at junctions of diffused interfaces via the vector-valued Allen--Cahn equation. We begin with the simplest case of a triple junction on the plane and present in detail a rigorous derivation in the case of triple and quadruple junctions in three-dimensional space. As a conclusion, we discuss some aspects of the related problem of deriving Plateau's laws from static balance of forces relations.