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A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
Group field theories are a generalization of matrix models which provide both a second quantized reformulation of loop quantum gravity as well as generating functions for spin foam models. While states in canonical loop quantum gravity, in…
The infinite group of deformed diffeomorphisms of the spacetime continuum is put into the basis of the gauge theory of gravity. This gives rise to some new ways for unification of gravity with other gauge interactions.
Conservation laws in gravitational theories with diffeomorphism and local Lorentz symmetry are studied. Main attention is paid to the construction of conserved currents and charges associated with an arbitrary vector field that generates a…
The treatment of exact conservation laws in Lagrangian gauge theories constitutes the main axis of the first part of the thesis. The formalism is developed as a self-consistent theory but is inspired by earlier works, mainly by…
Gauge theories are important descriptions for many physical phenomena and systems in quantum computation. Automorphism of gauge group naturally gives global symmetries of gauge theories. In this work we study such symmetries in gauge…
Based on a fundamental symmetry between space, time, mass and charge, a series of group structures of physical interest is generated, ranging from C2 to E8. The most significant result of this analysis is a version of the Dirac equation…
According to our microscopic cosmological model, masses of charged leptons can be calculated by curvatures of hyper-spherical surfaces embedded in a 3D time-like subspace. In this study, a higher-dimensional Lagrangian representation is…
Group field theories are quantum field theories built on groups. They can be seen as a tool to generate topological state-sums or quantum gravity models. For four dimensional manifolds, different arguments have pointed towards 2-groups…
Dimensional reduction of (super-)gravity theories to 3 dimensions results in sigma models on coset spaces G/H, such as the E_8/SO(16) coset in the bosonic sector of 3 dimensional maximal supergravity. The reverse process, oxidation, is the…
Applying recursive renormalization group transformations to a scalar field theory, we obtain an effective quantum gravity theory with an emergent extra dimension, described by a dual holographic Einstein-Klein-Gordon type action. Here, the…
We identify a class of condensate states in the group field theory (GFT) approach to quantum gravity that can be interpreted as macroscopic homogeneous spatial geometries. We then extract the dynamics of such condensate states directly from…
Let G be a finitely generated discrete group. The standard spectral triple on the group C*-algebra C*(G) is shown to admit the quantum group of orientation preserving isometries. This leads to new examples of compact quantum groups. In…
In this paper we first show that any coupled system consisting of a gravitational plus a free electromagnetic field can be described geometrically in the sense that both Maxwell equations and Einstein equation having as source term the…
Universal coverings of the orthogonal groups and their extensions are studied in terms of Clifford-Lipschitz groups. An algebraic description of basic discrete symmetries (space inversion $P$, time reversal $T$, charge conjugation $C$ and…
Unified field theories act to merge the internal symmetries of the standard model into a single group. Here we lay out something different. That is, instead of aiming to unify the internal symmetries, we demonstrate a sense in which the…
Cartan geometry provides a unifying algebraic construction of curvature and torsion, based on an underlying model Lie algebra -- a viewpoint that can be extended naturally to the higher algebraic structures underlying supergravity. We…
The thesis is divided into two parts. In the first part the low-energy limit of quantum gravity is analysed, whereas in the second we deal with the high-energy domain. In the first part, by applying the effective field theory point of view…
In four space-time dimensions General Relativity can be non-trivially deformed. Deformed theories continue to describe two propagating degrees of freedom, as GR. We study Euclidean black hole thermodynamics in these deformations. We use the…
We explore an extension of the symmetric teleparallel gravity denoted the $f(Q)$ theory, by considering a function of the nonmetricity invariant $Q$ as the gravitational Lagrangian. Some interesting properties could be found in the $f(Q)$…