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.
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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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