Spectral Theory of Automorphism Groups and Particle Structures in Quantum Field Theory
| dc.creator | Dybalski, Wojciech | |
| dc.date | 2009-01-20 | |
| dc.date.accessioned | 2026-07-07T12:34:07Z | |
| dc.date.available | 2026-07-07T12:34:07Z | |
| dc.description | 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. | |
| dc.description | PhD thesis, University of Goettingen, 2008 (advisor D. Buchholz) 156 pages | |
| dc.identifier | https://arxiv.org/abs/0901.3127 | |
| dc.identifier | http://arxiv.org/abs/0901.3127 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/217309 | |
| dc.subject | Mathematical Physics | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Spectral Theory of Automorphism Groups and Particle Structures in Quantum Field Theory | |
| dc.type | text |