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We study a physically motivated representation of an algebra of operators in gravitational and non gravitational theories called the covariant representation of an algebra. This is a representation where the symmetries of the operator…
Starting from a parameterisation of the quantum effective action for gravity we calculate correlation functions for observable quantities. The resulting templates allow to reverse-engineer the couplings describing the effective dynamics…
Non-relativistic quantum mechanics is reformulated here based on the idea that relational properties among quantum systems, instead of the independent properties of a quantum system, are the most fundamental elements to construct quantum…
In this article, the quantum representation of the algebra among reduced twisted geometries (with respect to the Gauss constraint) is constructed in the gauge invariant Hilbert space of loop quantum gravity. It is shown that the reduced…
We give a standard introduction to loop quantum gravity, from the ADM variables to spin network states. We include a discussion on quantum geometry on a fixed graph and its relation to a discrete approximation of general relativity.
Quantum Field Theory (QFT) represents a vast generalization of Quantum Mechanics (QM), as it deals with systems that have an infinite number of degrees of freedom. The Stone-von Neumann theorem, which establishes the equivalence of…
We derive an effective gravitational potential, induced by the quantum wavefunction of a physical vacuum of a self-gravitating configuration, while the vacuum itself is viewed as the superfluid described by the logarithmic quantum wave…
The quantum field algebra of real scalar fields is shown to be an example of infinite dimensional quantum group. The underlying Hopf algebra is the symmetric algebra S(V) and the product is Wick's normal product. Two coquasitriangular…
We formulate quantum gravity in $2+\epsilon$ dimensions in such a way that the conformal mode is explicitly separated. The dynamics of the conformal mode is understood in terms of the oversubtraction due to the one loop counter term. The…
We relate three-dimensional loop quantum gravity to the combinatorial quantisation formalism based on the Chern-Simons formulation for three-dimensional Lorentzian and Euclidean gravity with vanishing cosmological constant. We compare the…
Loop Quantum Gravity is now a well established approach to quantum gravity. One of the main challenges still faced by the theory is constructing a consistent dynamics which would lead back to the standard dynamics of the gravitational field…
We consider the quantization of space-times which can possess different topologies within a symmetry reduced version of Wheeler-DeWitt theory. The quantum states are defined from a natural decomposition as an outer-product of a topological…
In this paper, classical gravity is reformulated in terms of loops, via an algebraic topological approach. The main component is the loop group, whose elements consist of pairs of cobordant loops. A Chas-Sullivan product is described on the…
Since the gauge group underlying 2+1-dimensional general relativity is non-compact, certain difficulties arise in the passage from the connection to the loop representations. It is shown that these problems can be handled by appropriately…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
We construct a state in the loop quantum gravity theory with zero cosmological constant, which should correspond to the flat spacetime vacuum solution. This is done by defining the loop transform coefficients of a flat connection…
We introduce a vertex amplitude for 4d loop quantum gravity. We derive it from a conventional quantization of a Regge discretization of euclidean general relativity. This yields a spinfoam sum that corrects some difficulties of the…
We introduce a novel method for computing entanglement entropy across surfaces in Loop Quantum Gravity by employing techniques from quantum error correcting codes. In this construction, the redundancy encoded in the gauge invariant subspace…
It is shown that the Riemannian curvature of the 3-dimensional hypersurfaces in space-time, described by the Wilson loop integral, can be represented by a quaternion quantum operator induced by the SU(2) gauge potential, thus providing a…
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…