Related papers: Spinor Representation for Loop Quantum Gravity
Recently the $\text{SU}(2)$ spin-network states in loop quantum gravity is generalized to those of the corresponding affine Lie algebra. We show that if one literally starts from the full $\text{SL}(2,\mathbb{C})$ group, this procedure…
In the search for a covariant formulation for Loop Quantum Gravity, spin foams have arised as the corresponding discrete space-time structure and, among the different models, the Barrett-Crane model seems the most promising. Here, we study…
Multipartite generalizations of spin coherent states are introduced and analyzed. These are the spin analogues of multimode optical coherent states as used in continuous variable quantum information, but generalized to possess full spin…
Spherically symmetric models of loop quantum gravity have been studied recently by different methods that aim to deal with structure functions in the usual constraint algebra of gravitational systems. As noticed by Gambini and Pullin, a…
Reporting about the Wigner formalism for describing Dirac spinor structures through a covariant phase-space formulation, the quantum information quantifiers for purity and mutual information involving spin-parity (discrete) and…
We present a straightforward and self-contained introduction to the basics of the loop approach to quantum gravity, and a derivation of what is arguably its key result, namely the spectral analysis of the area operator. We also discuss the…
The conventional role of spacetime geometry in the description of gravity is pointed out. Global Poincar$\acute{\mbox{e}}$ symmetry as an inner symmetry of field theories defined on a fixed Minkowski spacetime is discussed. Its extension to…
We discuss the relation between coarse-graining and the holographic principle in the framework of loop quantum gravity and ask the following question: when we coarse-grain arbitrary spin network states of quantum geometry, are we…
We study the quantization of spherically symmetric vacuum spacetimes within loop quantum gravity. In particular, we give additional details about our previous work in which we showed that one could complete the quantization the model and…
Loop quantum gravity has provided us with a canonical framework especially devised for background independent and diffeomorphism invariant gauge field theories. In this quantization the fundamental excitations are called spin network…
Building on the universal covering group of the general linear group, we introduce the composite spinor bundle whose subbundles are Lorentz spin structures associated with different gravitational fields. General covariant transformations of…
We discuss the extension of loop quantum gravity to topspin networks, a proposal which allows topological information to be encoded in spin networks. We will show that this requires minimal changes to the phase space, C*-algebra and Hilbert…
The canonical quantization of diffeomorphism invariant theories of connections in terms of loop variables is revisited. Such theories include general relativity described in terms of Ashtekar-Barbero variables and extension to Yang-Mills…
We reassess the problem of separability of the kinematic Hilbert space in loop quantum gravity under a new mathematical point of view. We use the formalism of frames, a tool used in signal analysis, in order to remove the redundancy of the…
The aim of this paper is to discuss a kinematical algebraic structure of a theory of gravity, that would be unitary, renormalizable and coupled in the same manner to both spinorial and tensorial matter fields. An analysis of the common…
In this paper, we adapt the characterisation of the spin representation via exterior forms to the generalised spin$^r$ context. We find new invariant spin$^r$ spinors on the projective spaces $\mathbb{CP}^n$, $\mathbb{HP}^n$, and the Cayley…
The three-dimensional universal complex Clifford algebra is used to represent relativistic vectors in terms of paravectors. In analogy to the Hestenes spacetime approach spinors are introduced in an algebraic form. This removes the…
We derive a spacetime formulation of quantum general relativity from (hamiltonian) loop quantum gravity. In particular, we study the quantum propagator that evolves the 3-geometry in proper time. We show that the perturbation expansion of…
We describe fundamental equations which define the topological ground states in the lattice realization of the SU(2) BF phase. We introduce a new scalar Hamiltonian, based on recent works in quantum gravity and topological models, which is…
$SU(\infty)-QGR$ is a foundationally quantum approach to cosmology and gravity. It assumes that the Hilbert space of the Universe as a whole represents the symmetry group $SU(\infty)$, and demonstrates this symmetry for Hilbert spaces of…