Related papers: A monoidal representation for linearized gravity
In this paper we have applied Bohmian quantum theory to the linear field approximation of gravity and present a self--consistent quantum gravity theory in the linear field approximation. The theory is then applied to some specific problems,…
We study the loop representation of the quantum theory for 2+1 dimensional general relativity on a manifold, $M = {\cal T}^2 \times {\cal R}$, where ${\cal T}^2$ is the torus, and compare it with the connection representation for this…
We study the algebra of constraints of quantum gravity in the loop representation based on Ashtekar's new variables. We show by direct computation that the quantum commutator algebra reproduces the classical Poisson bracket one, in the…
Vielbeins are necessary when coupling General Relativity (GR) to fermionic matter. This enhances the gauge group of GR to include local Lorentz transformations. In view of a reduced phase space formulation of quantum gravity, in this work…
We present a line by line derivation of canonical quantum mechanics stemming from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This viewpoint can…
In quantum gravity, one looks for alternative structures to spacetime physics than ordinary real manifolds. Here, we propose an alternative universal construction containing the latter as an equilibrium state under the action of the…
We show that the Hamiltonian of four-dimensional Lorentzian gravity, defined on a space of real, SU(2)-valued connections, in spite of its non-polynomiality possesses a natural quantum analogue in a lattice-discretized formulation of the…
We consider a twisted version of quantum groups corepresentations. This generalization amounts to include in the theory the case where quantum space coordinates and its endomorphism matrix entries belong to a non-commutative quadratic…
Exactly soluble models can serve as excellent tools to explore conceptual issues in non-perturbative quantum gravity. In perturbative approaches, it is only the two radiative modes of the linearized gravitational field that are quantized.…
A recent paper promises new constructions that may make it possible to achieve covariance in spherically symmetric models of loop quantum gravity. This claim is contrary to the discovery of several stubborn obstacles to covariance uncovered…
We quantize the Maxwell theory in the presence of a electric charge in a "dual" Loop Representation, i.e. a geometric representation of magnetic Faraday's lines. It is found that the theory can be seen as a theory without sources, except by…
Borrowing ideas from the relation between simply laced Lie algebras and Dynkin diagrams, a weighted graph theory representation of quantum information is addressed. In this way, the density matrix of a quantum state can be interpreted as a…
In canonical gravity, general covariance is implemented by hypersurface-deformation symmetries on phase space. The different versions of hypersurface deformations required for full covariance have complicated interplays with one another,…
We study generalized electric/magnetic duality in Abelian gauge theory by combining techniques from locally covariant quantum field theory and Cheeger-Simons differential cohomology on the category of globally hyperbolic Lorentzian…
The gravity is classically formulated as the geometric curvature of the space-time in general relativity which is completely different from the other well-known physical forces. Since seeking a quantum framework for the gravity is a great…
The non-linear realisation based on $A_1^{+++}$ is known to describe gravity in terms of both the graviton and the dual graviton. We extend this analysis at the linearised level to find the equations of motion for the first higher dual…
We will construct a loop space formalism for general relativity, and construct the Polyakov variables as connections for such a loop space. We will use these Polyakov variables to construct a dual theory of gravity beyond linear…
The concept of electric-magnetic duality can be extended to linearized gravity. It has indeed been established that in four dimensions, the Pauli-Fierz action (quadratic part of the Einstein-Hilbert action) can be cast in a form that is…
The philosophy of the Loop Quantum Gravity approach is to construct the canonical variables by using the duality of infinitesimal connections and holonomies along loops. Based on this fundamental property for example the holonomy-flux…
The inclusion of matter fields in spherically symmetric loop quantum gravity has proved problematic at the level of implementing the constraint algebra including the Hamiltonian constraint. Here we consider the system with the introduction…