Related papers: Topological quantum field theory and quantum gravi…
This paper is a follow-up to a previous paper on fermions. A simple state sum model for a scalar field on a triangulated 1-manifold is constructed. The model is independent of the triangulation and gives exactly the same partition function…
This thesis discusses the topological aspects of quantum gravity, focusing on the connection between 2D quantum gravity and 2D topological gravity. The mathematical background for the discussion is presented in the first two chapters. The…
The physics of quantum gravity is discussed within the framework of topological quantum field theory. Some of the principles are illustrated with examples taken from theories in which space-time is three dimensional.
We give a very concise review of the group field theory formalism for non-perturbative quantum gravity, a higher dimensional generalisation of matrix models. We motivate it as a simplicial and local realisation of the idea of 3rd…
A link between canonical quantum gravity and fermionic quantum field theory is established in this paper. From a spectral triple construction which encodes the kinematics of quantum gravity semi-classical states are constructed which, in a…
It is argued that quantum gravity has an interpretation as a topological field theory provided a certain constraint from the path intergral measure is respected. The constraint forces us to couple gauge and matter fields to gravity for…
This thesis provides an introduction to the various category theory ideas employed in topological quantum field theory. These theories are viewed as symmetric monoidal functors from topological cobordism categories into the category of…
"Quantum Topology" deals with the general quantum theory as the theory of the functional quantum space; space time and energy momentum forms form a connected manifold; a functional quantum space on the quantum level. The general quantum…
The first part of this work deals with the development of a natural differential calculus on non-commutative manifolds. The second part extends the covariance and equivalence principle as well studies its kinematical consequences such as…
By considering specific limits in the gauge coupling constant of pure Yang--Mills dynamics, it is shown how there exist topological quantum field theory sectors in such systems defining nonperturbative topological configurations of the…
A simple state sum model for fermions on a 1-manifold is constructed. The model is independent of the triangulation and gives exactly the same partition function as the Dirac functional integral with zeta-function regularisation. Some…
We study the quantum mechanics of a system of topologically interacting particles in 2+1 dimensions, which is described by coupling the particles to a Chern-Simons gauge field of an inhomogeneous group. Analysis of the phase space shows…
It is shown how to write the first order action for gravity in a gauge theoretic formalism where the spin connection and frame field degrees of freedom are assimilated together into a gauge connection. It is then shown how to couple the…
This paper reviews the construction of quantum field theory on a 4-dimensional spacetime by combinatorial methods, and discusses the recent developments in the direction of a combinatorial construction of quantum gravity.
The main results for the two-dimensional quantum gravity, conjectured from the matrix model or integrable approach, are presented in the form to be compared with the world-sheet or Liouville approach. In spherical limit the integrable side…
This is an introduction to the group field theory approach to quantum gravity, with emphasis on motivations and basic formalism, more than on recent results; we elaborate on the various ingredients, both conceptual and formal, of the…
We provide a rather extended introduction to the group field theory approach to quantum gravity, and the main ideas behind it. We present in some detail the GFT quantization of 3d Riemannian gravity, and discuss briefly the current status…
A new method for nonperturbative investigations of quantum gravity is presented in which the simplicial path integral is approximated by the partition function of a spin system. This facilitates analytical and numerical computations…
We construct a topological field theory which, on the one hand, generalizes BF theories in that there is non-trivial coupling to `topological matter fields'; and, on the other, generalizes the three-dimensional model of Carlip and Gegenberg…
In this thesis we investigate topological aspects and arithmetic structures in quantum field theory and string theory. Particular focus is put on consistent truncations of supergravity and compactifications of F-theory.