@phdthesis{Kegeles2018,
  author    = {Kegeles, Alexander},
  title     = {Algebraic foundation of Group Field Theory},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-421014},
  school      = {Universit{\"a}t Potsdam},
  pages     = {124},
  year      = {2018},
  abstract  = {In this thesis we provide a construction of the operator framework starting from the functional formulation of group field theory (GFT). We define operator algebras on Hilbert spaces whose expectation values in specific states provide correlation functions of the functional formulation. Our construction allows us to give a direct relation between the ingredients of the functional GFT and its operator formulation in a perturbative regime. Using this construction we provide an example of GFT states that can not be formulated as states in a Fock space and lead to math- ematically inequivalent representations of the operator algebra. We show that such inequivalent representations can be grouped together by their symmetry properties and sometimes break the left translation symmetry of the GFT action. We interpret these groups of inequivalent representations as phases of GFT, similar to the classification of phases that we use in QFT's on space-time.},
  language  = {en}
}