@article{KegelesOriti2017,
  author    = {Kegeles, Alexander and Oriti, Daniele},
  title     = {Continuous point symmetries in group field theories},
  series = {Journal of physics : A, Mathematical and theoretical},
  volume    = {50},
  journal   = {Journal of physics : A, Mathematical and theoretical},
  number    = {12},
  publisher = {IOP Publishing Ltd},
  address   = {Bristol},
  issn      = {1751-8113},
  doi       = {10.1088/1751-8121/aa5c14},
  pages     = {36},
  year      = {2017},
  abstract  = {We discuss the notion of symmetries in non-local field theories characterized by integro-differential equations of motion, from a geometric perspective. We then focus on group field theory (GFT) models of quantum gravity and provide a general analysis of their continuous point symmetry transformations, including the generalized conservation laws following from them.},
  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}
}
@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}
}