Related papers: Three Dimensional Loop Quantum Gravity: Particles …
The Hilbert space of loop quantum gravity is usually described in terms of cylindrical functionals of the gauge connection, the electric fluxes acting as non-commuting derivation operators. It has long been believed that this…
We perform the momentum-space quantization of a spin-less particle moving on the $SU(2)$ group manifold, that is, the three-dimensional sphere $S^{3}$, by using a non-canonical method entirely based on symmetry grounds. To achieve this…
States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K\"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics…
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corresponding to areas of 2-surfaces…
If quantum gravity respects the principles of quantum mechanics, suitably generalized, it may be that a more viable approach to the theory is through identifying the relevant quantum structures rather than by quantizing classical spacetime.…
Motivated by the construction of spectral manifolds in noncommutative geometry, we introduce a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of scalar fields. This commutation relation…
Two sets of spatially diffeomorphism invariant operators are constructed in the loop representation formulation of quantum gravity. This is done by coupling general relativity to an anti- symmetric tensor gauge field and using that field to…
After motivating why the study of asymptotically flat spaces is important in loop quantum gravity, we review the extension of the standard framework of this theory to the asymptotically flat sector based on the GNS construction. In…
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…
We analyze the phase space of gravity non-minimally coupled to a scalar field in a generic local Lorentz frame. We reduce the set of constraints to a first-class one by fixing a specific hypersurfaces in the phase space. The main issue of…
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 present a covariant quantum formalism for scalar particles based on an enlarged Hilbert space. The particular physical theory can be introduced through a timeless Wheeler DeWitt-like equation, whose projection onto four-dimensional…
We comment on structural properties of the algebras $\mathfrak{A}_{LQG/LQC}$ underlying loop quantum gravity and loop quantum cosmology, especially the representation theory, relating the appearance of the (dynamically induced)…
In physics, experiments ultimately inform us as to what constitutes a good theoretical model of any physical concept: physical space should be no exception. The best picture of physical space in Newtonian physics is given by the…
In this note, we attempt to provide some insights into the structure of non-perturbative descriptions of quantum gravity using known examples of gauge-theory / gravity duality. We argue that in familiar examples, a quantum description of…
We explain how quantum gravity can be defined by quantizing spacetime itself. A pinpoint is that the gravitational constant G = L_P^2 whose physical dimension is of (length)^2 in natural unit introduces a symplectic structure of spacetime…
We present a new group field theory describing 3d Riemannian quantum gravity coupled to matter fields for any choice of spin and mass. The perturbative expansion of the partition function produces fat graphs colored with SU(2) algebraic…
We study two-dimensional quantum gravity on arbitrary genus Riemann surfaces in the Kaehler formalism where the basic quantum field is the (Laplacian of the) Kaehler potential. We do a careful first-principles computation of the fixed-area…
Building on prior work, a generally covariant reformulation of free scalar field theory on the flat Lorentzian cylinder is quantized using Loop Quantum Gravity (LQG) type `polymer' representations. This quantization of the {\em continuum}…
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…