Related papers: Non-perturbative summation over 3D discrete topolo…
Group field theories represent a 2nd quantized reformulation of the loop quantum gravity state space and a completion of the spin foam formalism. States of the canonical theory, in the traditional continuum setting, have support on graphs…
Within the superfield formalism, we study the ultraviolet properties of the three-dimensional supersymmetric quantum electrodynamics. The theory is shown to be finite at all loops orders in a particular gauge.
In this article,we investigate some features of the perturbation theory in spatially closed universe. We will show that the perturbative field equations in a spatially closed universe always have two independent adiabatic solutions provided…
I define a model of three-dimensional simplicial gravity using an extended ensemble of triangulations where, in addition to the usual combinatorial triangulations, I allow degenerate triangulations, i.e. triangulations with distinct…
Let G be a discrete group. We give methods to compute for a generalized (co-)homology theory its values on the Borel construction (EG x X)/G of a proper G-CW-complex X satisfying certain finiteness conditions. In particular we give formulas…
I argue that the complete partition function of 3D quantum gravity is given by a path integral over gauge-inequivalent manifolds times the Chern-Simons partition function. In a discrete version, it gives a sum over simplicial complexes…
The gravitational clustering of collisionless particles in an expanding universe is modelled using some simple physical ideas. I show that it is indeed possible to understand the nonlinear clustering in terms of three well defined regimes:…
Partially massless theory in three dimensions is revisited and its relationship with the self-dual massive gravity is considered. The only mode of the partially massless theory is shown explicitly through an action for a scalar field on…
A formula is proposed for continuing physical correlation functions to non-integer numbers of dimensions, expressing them as infinite weighted sums over the same correlation functions in arbitrary integer dimensions. The formula is…
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…
We study non-perturbative quantization of 3d gravity with positive cosmological constant (de Sitter space being the prototype vacuum solution, whose Euclideanization of course gives the three sphere) on the background topology of lens…
For a wide class of nonlinear equations a perturbative solution is constructed. This class includes equations of motion of field theories. The solution possesses a graphical representation in terms of diagrams. To illustrate the formalism…
A gravitational field can be defined in terms of a moving frame, which when made noncommutative yields a preferred basis for a differential calculus. It is conjectured that to a linear perturbation of the commutation relations which define…
In this review we describe a non-trivial relationship between perturbative gauge theory and gravity scattering amplitudes. At the semi-classical or tree level, the scattering amplitudes of gravity theories in flat space can be expressed as…
The difficulties of perturbation theory associated with unstable fundamental fields (such as the lack of exact gauge invariance in each order) are cured if one constructs perturbative expansion directly for probabilities interpreted as…
We analyze in full mathematical rigor the most general quartically perturbed invariant probability measure for a random tensor. Using a version of the Loop Vertex Expansion (which we call the mixed expansion) we show that the cumulants…
A set of observables is described for the topological quantum field theory which describes quantum gravity in three space-time dimensions with positive signature and positive cosmological constant. The simplest examples measure the…
A non-perturbative method which can go beyond the weak coupling perturbation theory is introduced. Essential idea is to formulate a set of exact differential equations as a function of the coupling strength $g$. Unlike other resummation in…
We consider the coupling between three dimensional gravity with zero cosmological constant and massive spinning point particles. First, we study the classical canonical analysis of the coupled system. Then, we go to the Hamiltonian…
Borel summable semiclassical expansions in 1D quantum mechanics are considered. These are the Borel summable expansions of fundamental solutions and of quantities constructed with their help. An expansion, called topological,is constructed…