Related papers: New volume and inverse volume operators for loop q…
A new symmetric Hamiltonian constraint operator is proposed for loop quantum gravity, which is well defined in the Hilbert space of diffeomorphism invariant states up to non-planar vertices with valence higher than three. It inherits the…
A covariant spin-foam formulation of quantum gravity has been recently developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity. In particular, the geometrical observable giving the area…
This is the second paper in the series to introduce a graphical method to loop quantum gravity. We employ the graphical method as a powerful tool to calculate the actions of the Euclidean Hamiltonian constraint operator and the so-called…
A new local and gauge invariant quantum vortex operator is constructed in three-dimensional gauge field theories. The correlation functions of this operator are evaluated exactly in pure Maxwell theory and by means of a loop expansion in…
Volume operators measuring the total volume of space in a loop quantum theory of cosmological models are constructed. In the case of models with rotational symmetry an investigation of the Higgs constraint imposed on the reduced connection…
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…
Since there are quantization ambiguities in constructing the Hamiltonian constraint operator in isotropic loop quantum cosmology, it is crucial to check whether the key features of loop quantum cosmology, such as the quantum bounce and…
We present the construction of a physical Hamiltonian operator in the deparametrized model of loop quantum gravity coupled to a free scalar field. This construction is based on the use of the recently introduced curvature operator, and on…
We investigate the spectral properties of the volume operator in quantum gravity in the framework of a previously introduced lattice discretization. The presence of a well-defined scalar product in this approach permits us to make definite…
In Loop Quantum Gravity, the quantum action of the volume operator is crucial in understanding quantum dynamics. In this work, we implement a generalized numerical algorithm that can compute the quantum action of the volume operator on a…
The search for a quantum theory of gravity is one of the major challenges facing theoretical physics today. While no complete theory exists, a promising avenue of research is the loop quantum gravity approach. In this approach, quantum…
The properties of the Volume operator in Loop Quantum Gravity, as constructed by Ashtekar and Lewandowski, are analyzed for the first time at generic vertices of valence greater than four. The present analysis benefits from the general…
We present a generalization of the quantum volume operator quantifying the volume in curved three-dimensional discrete geometries. In its standard form, the quantum volume operator is constructed from tetrahedra whose faces are endowed with…
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…
Although the Hamiltonian in quantum physics has to be a linear operator, it is possible to make quantum systems behave as if their Hamiltonians contained antilinear (i.e., semilinear or conjugate-linear) terms. For any given quantum system,…
We present a concrete and explicit construction of a new scalar constraint operator for loop quantum gravity. The operator is defined on the recently introduced space of partially diffeomorphism invariant states, and this space is preserved…
A functional calculus on the space of (generalized) connections was recently introduced without any reference to a background metric. It is used to continue the exploration of the quantum Riemannian geometry. Operators corresponding to…
We investigate some properties of geometric operators in canonical quantum gravity in the connection approach \`a la Ashtekar, which are associated with volume, area and length of spatial regions. We motivate the construction of analogous…
An angular momentum operator in loop quantum gravity is defined using spherically symmetric states as a non-rotating reference system. It can be diagonalized simultaneously with the area operator and has the familiar spectrum. The operator…
The volume operator is an important kinematical quantity in the non-perturbative approach to four-dimensional quantum gravity in the connection formulation. We give a general algorithm for computing its spectrum when acting on four-valent…