17.07.2014, 16:15 Uhr  –  Free University Berlin, Arnimallee 6, SR 031
Seminar "Topics in Geometric Analysis"

Claus Gerhardt and Apostolos Damialis

16:15 Uhr Claus Gerhardt (Heidelberg) A unified quantum theory: gravity interacting with Yang-Mills and spinor fields

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.

 
17:45 Uhr Apostolos Damialis (FU Berlin) Plateau's laws for diffused interfaces

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.

 
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