Related papers: Loop Representations for 2+1 Gravity on a Torus
We discuss how the theory of quantum cohomology may be generalized to ``gravitational quantum cohomology'' by studying topological sigma models coupled to two-dimensional gravity. We first consider sigma models defined on a general Fano…
We study the phase space structure and the quantization of a pointlike particle in 2+1 dimensional gravity. By adding boundary terms to the first order Einstein Hilbert action, and removing all redundant gauge degrees of freedom, we arrive…
This paper is the third in a series whose goal is to develop a fundamentally new way of viewing theories of physics. Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a…
The quantum properties of two-dimensional matter-dilaton gravity ---which includes a large family of actions for two-dimensional gravity (in particular, string-inspired models)--- are investigated. The one-loop divergences in linear…
It is shown that the finite dimensional ireducible representations of the quantum matrix algebra $ M_q(3) $ ( the coordinate ring of $ GL_q(3) $ ) exist only when q is a root of unity ( $ q^p = 1 $ ). The dimensions of these representations…
In three spacetime dimensions, general relativity becomes a topological field theory, whose dynamics can be largely described holographically by a two-dimensional conformal field theory at the ``boundary'' of spacetime. I review what is…
The implications of the SU(2) gauge fixing associated with the choice of invariant triads in Loop Quantum Cosmology are discussed for a Bianchi I model. In particular, via the analysis of Dirac brackets, it is outlined how the holonomy-flux…
We systematically determine the regular representations, quivers and representation type of all liftings of two-dimensional quantum linear spaces.
We perform the two loop level renormalization of quantum gravity in $2+\epsilon$ dimensions. We work in the background gauge whose manifest covariance enables us to use the short distance expansion of the Green's functions. We explicitly…
A new link between tetrahedra and the group SU(2) is pointed out: by associating to each face of a tetrahedron an irreducible unitary SU(2) representation and by imposing that the faces close, the concept of quantum tetrahedron is seen to…
A symmetry extending the $T^2$-symmetry of the noncommutative torus $T^2_q$ is studied in the category of quantum groups. This extended symmetry is given by the quantum double-torus defined as a compact matrix quantum group consisting of…
A model for 2D-quantum gravity from the Virasoro symmetry is studied. The notion of space-time naturally arises as a homogeneous space associated with the kinematical (non-dynamical) SL(2,R) symmetry in the kernel of the Lie-algebra central…
The Hamiltoinian analysis of the vector-tensor theory of gravity is performed. The resulting geometrical dynamics is reformulated into the connection dynamics, with the real SU(2)-connection serving as one of the configuration variables.…
The canonical ``loop'' formulation of quantum gravity is a mathematically well defined, background independent, non perturbative standard quantization of Einstein's theory of General Relativity. Some among the most meaningful results of the…
Witten described how a path integral quantization of Wilson Loop observables will define Jones polynomial type of link invariants, using the Chern-Simons gauge theory in $\mathbb{R}^3$. In this gauge theory, a compact Lie group ${\rm G}$,…
The 2D gravity described by the action which is an arbitrary function of the scalar curvature $f(R)$ is considered. The classical vacuum solutions are analyzed. The one-loop renormalizability is studied. For the function $f=R \ln R$ the…
The effects of spacetime quantization on black hole and big bang/big crunch singularities can be studied using new tools from (2+1)-dimensional quantum gravity. I investigate effects of spacetime quantization on singularities of the…
A quantization of (2+1)-dimensional gravity with negative cosmological constant is presented and quantum aspects of the (2+1)-dimensional black holes are studied thereby. The quantization consists of two procedures. One is related with…
Quantisation on spaces with properties of curvature, multiple connectedness and non orientablility is obtained. The geodesic length spectrum for the Laplacian operator is extended to solve the Schroedinger operator. Homotopy fundamental…
A general classical theorem is presented according to which all invariant relations among the space time metric scalars, when turned into functions on the Phase Space of full Pure Gravity (using the Canonical Equations of motion), become…