@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}
}
@phdthesis{Steinhaus2014,
  author    = {Steinhaus, Sebastian Peter},
  title     = {Constructing quantum spacetime},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72558},
  school      = {Universit{\"a}t Potsdam},
  year      = {2014},
  abstract  = {Despite remarkable progress made in the past century, which has revolutionized our understanding of the universe, there are numerous open questions left in theoretical physics. Particularly important is the fact that the theories describing the fundamental interactions of nature are incompatible. Einstein's theory of general relative describes gravity as a dynamical spacetime, which is curved by matter and whose curvature determines the motion of matter. On the other hand we have quantum field theory, in form of the standard model of particle physics, where particles interact via the remaining interactions - electromagnetic, weak and strong interaction - on a flat, static spacetime without gravity. A theory of quantum gravity is hoped to cure this incompatibility by heuristically replacing classical spacetime by quantum spacetime'. Several approaches exist attempting to define such a theory with differing underlying premises and ideas, where it is not clear which is to be preferred. Yet a minimal requirement is the compatibility with the classical theory, they attempt to generalize. Interestingly many of these models rely on discrete structures in their definition or postulate discreteness of spacetime to be fundamental. Besides the direct advantages discretisations provide, e.g. permitting numerical simulations, they come with serious caveats requiring thorough investigation: In general discretisations break fundamental diffeomorphism symmetry of gravity and are generically not unique. Both complicates establishing the connection to the classical continuum theory. The main focus of this thesis lies in the investigation of this relation for spin foam models. This is done on different levels of the discretisation / triangulation, ranging from few simplices up to the continuum limit. In the regime of very few simplices we confirm and deepen the connection of spin foam models to discrete gravity. Moreover, we discuss dynamical, e.g. diffeomorphism invariance in the discrete, to fix the ambiguities of the models. In order to satisfy these conditions, the discrete models have to be improved in a renormalisation procedure, which also allows us to study their continuum dynamics. Applied to simplified spin foam models, we uncover a rich, non--trivial fixed point structure, which we summarize in a phase diagram. Inspired by these methods, we propose a method to consistently construct the continuum theory, which comes with a unique vacuum state.},
  language  = {en}
}
@phdthesis{Sahlmann2002,
  author    = {Sahlmann, Hanno},
  title     = {Coupling matter to loop quantum gravity},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-0000602},
  school      = {Universit{\"a}t Potsdam},
  year      = {2002},
  abstract  = {Motiviert durch neuere Vorschl{\"a}ge zur experimentellen Untersuchung von Quantengravitationseffekten werden in der vorliegenden Arbeit Annahmen und Methoden untersucht, die f{\"u}r die Vorhersagen solcher Effekte im Rahmen der Loop-Quantengravitation verwendet werden k{\"o}nnen. Dazu wird als Modellsystem ein skalares Feld, gekoppelt an das Gravitationsfeld, betrachtet. Zun{\"a}chst wird unter bestimmten Annahmen {\"u}ber die Dynamik des gekoppelten Systems eine Quantentheorie f{\"u}r das Skalarfeld vorgeschlagen. Unter der Annahme, dass sich das Gravitationsfeld in einem semiklassischen Zustand befindet, wird dann ein \"QFT auf gekr{\"u}mmter Raumzeit-Limes\" dieser Theorie definiert. Im Gegensatz zur gew{\"o}hnlichen Quantenfeldtheorie auf gekr{\"u}mmter Raumzeit beschreibt die Theorie in diesem Grenzfall jedoch ein quantisiertes Skalarfeld, das auf einem (klassisch beschriebenen) Zufallsgitter propagiert. Sodann werden Methoden vorgeschlagen, den Niederenergieliemes einer solchen Gittertheorie, vor allem hinsichtlich der resultierenden modifizierten Dispersonsrelation, zu berechnen. Diese Methoden werden anhand von einfachen Modellsystemen untersucht. Schließlich werden die entwickelten Methoden unter vereinfachenden Annahmen und der Benutzung einer speziellen Klasse von semiklassischen Zust{\"a}nden angewandt, um Korrekturen zur Dispersionsrelation des skalaren und des elektromagnetischen Feldes im Rahmen der Loop-Quantengravitation zu berechnen. Diese Rechnungen haben vorl{\"a}ufigen Charakter, da viele Annahmen eingehen, deren G{\"u}ltigkeit genauer untersucht werden muss. Zumindest zeigen sie aber Probleme und M{\"o}glichkeiten auf, im Rahmen der Loop-Quantengravitation Vorhersagen zu machen, die sich im Prinzip experimentell verifizieren lassen.},
  language  = {en}
}
@article{KegelesOritiTomlin2018,
  author    = {Kegeles, Alexander and Oriti, Daniele and Tomlin, Casey},
  title     = {Inequivalent coherent state representations in group field theory},
  series = {Classical and quantum gravit},
  volume    = {35},
  journal   = {Classical and quantum gravit},
  number    = {12},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {0264-9381},
  doi       = {10.1088/1361-6382/aac39f},
  pages     = {23},
  year      = {2018},
  abstract  = {In this paper we propose an algebraic formulation of group field theory and consider non-Fock representations based on coherent states. We show that we can construct representations with an infinite number of degrees of freedom on compact manifolds. We also show that these representations break translation symmetry. Since such representations can be regarded as quantum gravitational systems with an infinite number of fundamental pre-geometric building blocks, they may be more suitable for the description of effective geometrical phases of the theory.},
  language  = {en}
}