@phdthesis{Raetzel2013,
  author    = {R{\"a}tzel, Dennis},
  title     = {Tensorial spacetime geometries and background-independent quantum field theory},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-65731},
  school      = {Universit{\"a}t Potsdam},
  year      = {2013},
  abstract  = {Famously, Einstein read off the geometry of spacetime from Maxwell's equations. Today, we take this geometry that serious that our fundamental theory of matter, the standard model of particle physics, is based on it. However, it seems that there is a gap in our understanding if it comes to the physics outside of the solar system. Independent surveys show that we need concepts like dark matter and dark energy to make our models fit with the observations. But these concepts do not fit in the standard model of particle physics. To overcome this problem, at least, we have to be open to matter fields with kinematics and dynamics beyond the standard model. But these matter fields might then very well correspond to different spacetime geometries. This is the basis of this thesis: it studies the underlying spacetime geometries and ventures into the quantization of those matter fields independently of any background geometry. In the first part of this thesis, conditions are identified that a general tensorial geometry must fulfill to serve as a viable spacetime structure. Kinematics of massless and massive point particles on such geometries are introduced and the physical implications are investigated. Additionally, field equations for massive matter fields are constructed like for example a modified Dirac equation. In the second part, a background independent formulation of quantum field theory, the general boundary formulation, is reviewed. The general boundary formulation is then applied to the Unruh effect as a testing ground and first attempts are made to quantize massive matter fields on tensorial spacetimes.},
  language  = {en}
}
@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}
}