Related papers: Canonical quantization of non-commutative holonomi…
We start with the Hamiltonian formulation of the first order action of pure gravity with a full $\mathfrak{sl}(2,\mathbb C)$ internal gauge symmetry. We make a partial gauge-fixing which reduces $\mathfrak{sl}(2,\mathbb C)$ to its…
We define a theory of Galilean gravity in 2+1 dimensions with cosmological constant as a Chern-Simons gauge theory of the doubly-extended Newton-Hooke group, extending our previous study of classical and quantum gravity in 2+1 dimensions in…
Canonical methods can be used to construct effective actions from deformed covariance algebras, as implied by quantum-geometry corrections of loop quantum gravity. To this end, classical constructions are extended systematically to…
There is a surge of research devoted to the formalism and physical manifestations of non-Lorentzian kinematical symmetries, which focuses especially on the ones associated with the Galilei and Carroll relativistic limits (the speed of light…
We propose an exact Hamiltonian lattice theory for (2+1)-dimensional spacetimes with homogeneous curvature. By gauging away the lattice we find a generalization of the ``polygon representation'' of (2+1)-dimensional gravity. We compute the…
We advocate an alternative description of canonical gravity in 3+1 dimensions, obtained by using as the basic variable a real variant of the usual Ashtekar connection variables on the spatial three-manifold. With this ansatz, no non-trivial…
We describe a program for developing a canonical gravity in 2+2 dimensions (two time and two space dimensions). Our procedure is similar to the usual canonical gravity but with two times rather than just one time. Our work may be of…
Loop quantum cosmology is a symmetry reduced quantization of cosmological spacetimes based on loop quantum gravity. While it has been successful in resolution of various cosmological singularities and connecting Planck scale physics to…
As a canonical and generally covariant gauge theory, loop quantum gravity requires special techniques to derive effective actions or equations. If the proper constructions are taken into account, the theory, in spite of considerable…
In a previous work [arXiv:2009.03428] we proposed a new model for Quantum GRavity(QGR) and cosmology, dubbed $SU(\infty)$-QGR. One of the axioms of this model is that Hilbert spaces of the Universe and its subsystems represent $SU(\infty)$…
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…
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…
Loop quantum gravity is an approach to quantum gravity that starts from the Hamiltonian formulation in terms of a connection and its canonical conjugate. Quantization proceeds in the spirit of Dirac: First one defines an algebra of basic…
Based on a recent purely geometric construction of observables for the spatial diffeomorphism constraint, we propose two distinct quantum reductions to spherical symmetry within full 3+1-dimensional loop quantum gravity. The construction of…
We do not yet know how to quantize gravity in 3+1 dimensions, but in lower dimensions we face the opposite problem: many of the approaches originally developed for (3+1)-dimensional gravity can be successfully implemented in 2+1 dimensions,…
We derive the Gauss-Codazzi equation in the holonomy and plane-angle representations and we use the result to write a Gauss-Codazzi equation for a discrete (2+1)-dimensional manifold, triangulated by isosceles tetrahedra. This allows us to…
Inspired by the long wave-length limit of topological M-theory, which re-constructs the theory of $3+1$D gravity in the self-dual variables' formulation, we conjecture the existence of a duality between Hilbert spaces, the ${\bf…
We discuss the canonical quantization of Quantum Electrodynamics in $2+1$ dimensions, with a Chern-Simons topological mass term and gauge-covariant coupling to a Dirac spinor field. A gauge-fixing term is used which generates a canonical…
We use the polygon representation of 2+1--dimensional gravity to explicitly carry out the canonical quantization of a universe with the topology of a torus. The mapping-class-invariant wave function for a quantum ''big bounce'', is…
In this paper, I investigate the quantisation of length in euclidean quantum gravity in three dimensions. The starting point is the classical hamiltonian formalism in a cylinder of finite radius. At this finite boundary, a counter term is…