Spectral Theory of Automorphism Groups and Particle Structures in Quantum Field Theory

Abstract

This Thesis presents some physically motivated criteria for the existence of particles and infra-particles in a given quantum field theory. It is based on a refined spectral theory of automorphism groups describing the energy-momentum transfer of local observables. In particular, a novel decomposition of the algebra of local observables into spectral subspaces is constructed. Apart from the counterparts of the pure-point and absolutely continuous subspaces, familiar from the spectral theory of operators, there appears a new 'point-continuous' subspace. It belongs to the singular-continuous part of the decomposition, but is finite-dimensional in a large class of models; its dimension carries information about the infrared structure of a theory. It is shown that this point-continuous subspace is trivial in all theories complying with a regularity condition proposed in this work. Moreover, this condition entails the existence of particles if the theory admits a stress-energy tensor. The uniqueness of the decomposition of the algebra of observables into the pure-point and continuous subspace is established by proving an ergodic theorem for automorphism groups. The proof is based on physically motivated phase space conditions which have a number of interesting consequences pertaining to the vacuum structure such as the convergence of physical states to a unique vacuum under large timelike translations.

arXiv commentPhD thesis, University of Goettingen, 2008 (advisor D. Buchholz) 156 pages

References in corpus (9)

• Polarization-Free Generators and the S-Matrix
• Phase space properties and the short distance structure in quantum field theory
• Haag-Ruelle scattering theory in presence of massless particles
• Operator product expansions as a consequence of phase space properties
• Particle Weights and their Disintegration II
• Generalized fixed point algebras and square-integrable group actions
• On the manifestations of particles
• Phase Space Properties of Local Observables and Structure of Scaling Limits
• A sharpened nuclearity condition for massless fields

Cited by in corpus (2)

• Infraparticles with superselected direction of motion in two-dimensional conformal field theory
• Mourre theory and asymptotic observables in local relativistic quantum field theory