相关论文: Closed formula for the matrix elements of the volu…

Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and…

Quantum polyhedra constructed from angular momentum operators are the building blocks of space in its quantum description as advocated by Loop Quantum Gravity. Here we extend previous results on the semiclassical properties of quantum…

In a remarkable paper, T. Koslowski introduced kinematical representations for loop quantum gravity in which there is a non-degenerate spatial background metric present. He also considered their properties, and showed that Gauss and…

We construct a model of quantum gravity in which dimension, topology and geometry of spacetime are dynamical. The microscopic degree of freedom is a real rectangular matrix whose rows label internal flavours, and columns label spatial…

D = 2+1 gravity with a cosmological constant has been shown by Bonzom and Livine to present a Barbero-Immirzi like ambiguity depending on a parameter. We make use of this fact to show that, for positive cosmological constant, the Lorentzian…

We construct the regularised Wheeler-De Witt operator demanding that the algebra of constraints of quantum gravity is anomaly free. We find that for a subset of all wavefunctions being integrals of scalar densities this condition can be…

Physics in (canonical) quantum gravity needs to be manifestly diffeomorphism-invariant. Consequently, physical observables need to be formulated in terms of manifestly diffeomorphism-invariant operators, which are necessarily composite.…

A well-defined regularized path integral for Lorentzian quantum gravity in three and four dimensions is constructed, given in terms of a sum over dynamically triangulated causal space-times. Each Lorentzian geometry and its associated…

We present an explicit computation of matrix elements of the hamiltonian constraint operator in non-perturbative quantum gravity. In particular, we consider the euclidean term of Thiemann's version of the constraint and compute its action…

We show that the algebra of discretized spatial diffeomorphism constraints in Hamiltonian lattice quantum gravity closes without anomalies in the limit of small lattice spacing. The result holds for arbitrary factor-ordering and for a…

Inertial and gravitational mass or energy-momentum need not be the same for virtual quantum states. Separating their roles naturally leads to the gauge theory of volume-preserving diffeomorphisms of an inner four-dimensional space. The…

We construct and study Loop Quantum Cosmology (LQC) when the Barbero-Immirzi parameter takes the complex value $\gamma=\pm i$. We refer to this new quantum cosmology as complex Loop Quantum Cosmology. We proceed in making an analytic…

We present a simple method to calculate certain sums of the eigenvalues of the volume operator in loop quantum gravity. We derive the asymptotic distribution of the eigenvalues in the classical limit of very large spins which turns out to…

We review an attempt to set a suitable foundational principle for consistent quantization of gravity based on the canonical formulation. It requires extending the spacetime description of the relativistic postulates to also encompass an…

We formally prove the existence of a quantization procedure that makes the path integral of a general diffeomorphism-invariant theory of gravity, with fixed total spacetime volume, equivalent to that of its unimodular version. This is…

A fully consistent linear perturbation theory for cosmology is derived in the presence of quantum corrections as they are suggested by properties of inverse volume operators in loop quantum gravity. The underlying constraints present a…

An alternative expression for the length operator in loop quantum gravity is presented. The operator is background independent, symmetric, positive semidefinite, and well defined on the kinematical Hilbert space. The expression for the…

We present a quantization of the Hamiltonian and diffeomorphism constraint of canonical quantum gravity in the spin network representation. The novelty consists in considering a space of wavefunctions based on the Vassiliev knot invariants.…

We extend the definition of the "flipped" loop-quantum-gravity vertex to the case of a finite Immirzi parameter. We cover the Euclidean as well as the Lorentzian case. We show that the resulting dynamics is defined on a Hilbert space…

We present in the article the formulation of a version of Lorentz covariant quantum mechanics based on a group theoretical construction from a Heisenberg-Weyl symmetry with position and momentum operators transforming as Minkowski…