The physical interpretation of quantum field theories in terms of particles has been a fundamental long-standing issue. Due to the presence of complicated physical phenomena (e.g. pair creation, infraparticle problem), particle aspects are not fully under control even in simple models. Often it is not even clear what types of particles a given theory describes. However, a systematic study of these problems, pursued in the framework of algebraic quantum field theory, resulted in a model-independent procedure which unravels all the stable particle types. It turns out that further progress along these lines requires the development of new mathematical concepts in the field of spectral theory of automorphism groups. This book presents some recent advance in this challenging project. Centered on a novel spectral decomposition of the algebra of observables, it explores the problem of existence of particles and the vacuum structure in quantum field theory.

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