Wojciech Dybalski

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


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.