# Wojciech Dybalski

# Spectral analysis of C*-dynamical systems and particle aspects in QFT

** Abstract: **

The decomposition of the spectrum of a Hamiltonian
into its pure point, absolutely continuous and singular continuous
parts is crucial for the understanding of asymptotic completeness
in quantum mechanics. Therefore, a deeper understanding of particle
aspects in quantum field theory requires the development of a similar,
detailed spectral theory of C*-dynamical systems which describe
the spacetime translations of observables. This talk presents some
recent progress in this direction: A general framework for such analysis
is proposed and illustrated by several examples. Applications to the
problem of particle interpretation in QFT are discussed.