Related papers: Properties of the Volume Operator in Loop Quantum …
The core of quantum tomography is the possibility of writing a generally unbounded complex operator in form of an expansion over operators that are generally nonlinear functions of a generally continuous set of spectral densities--the…
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…
The phenomenology for the deep spatial geometry of loop quantum gravity is discussed. In the context of a simple model of an atom of space, it is shown how purely combinatorial structures can affect observations. The angle operator is used…
We apply the nonstandard loop quantum cosmology method to quantize a flat Friedmann-Robertson-Walker cosmological model with a free scalar field and the cosmological constant $\Lambda>0$. Modification of the Hamiltonian in terms of loop…
Quantum-reduced loop gravity is a model of loop quantum gravity, which - from the technical point of view - is characterized by the remarkably simple form of its basic operators. In this article we examine the operators of the…
We review recent work in the lattice approach to random surfaces and quantum gravity. Our task is made somewhat easier by some very interesting results, particularly in four dimensions, that have appeared recently and which are reported…
The question of general covariance in quantum gravity is considered in the first post-Newtonian approximation. Transformation properties of observable quantities under deformations of a reference frame, induced by variations of the gauge…
Based on the novel prescription for the power of a complex number, a new expression for the eigenfunction of the operator of the third component of the angular momentum is presented. These functions are normalizable, single valued and are…
We consider the eigenvalues of the three-dimensional Weyl operator defined in terms of the (Euclidean) Ashtekar variables, and we study their dependence on the gravitational field. We notice that these eigenvalues can be used as…
Spin Foam and Loop approaches to Quantum Gravity reformulate Einstein's theory of relativity in terms of connection variables. The metric properties are encoded in face bivectors/conjugate fluxes that are required to satisfy certain…
Loop quantum gravity admits a kind of area quantization that is characterized by three quantum numbers. We show the complete spectrum of area is the union of equidistant subsets and a universal reformulation with fewer parameters is…
I describe a possible perspective on the current state of loop quantum gravity, at the light of the developments of the last years. I point out that a theory is now available, having a well-defined background-independent kinematics and a…
We extend algorithmic information theory to quantum mechanics, taking a universal semicomputable density matrix (``universal probability'') as a starting point, and define complexity (an operator) as its negative logarithm. A number of…
The symplectic eigenvalues play a significant role in finite mode quantum information theory, and Williamson normal form proves to be a valuable tool in this area. Understanding the symplectic spectrum of a Gaussian Covariance Operator is a…
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…
Several proposals for Quantum Gravity involve length and area operators with discrete eigenvalues. I show that the analyses of some simple procedures for the measurement of areas and lengths suggest that this discreteness characterizing the…
Recently, we have shown how the interpretation of quantum mechanics due to Lande' can be used to derive from first principles generalized formulas for the operators and some eigenvectors for spin 1/2 Though we gave the operators for all the…
A set of diverse but mutually consistent results obtained in different settings has spawned a new view of loop quantum gravity and its physical implications, based on the interplay of operator calculations and effective theory: Quantum…
An analytically derived 'integral operator' approach is introduced to estimate the expectation value of a quantum operator for an evolving state weighted with an exponential function. This allows to compute quantities useful in Nuclear…
PDFs can be studied directly using lattice QCD by evaluating matrix elements of non-local operators. A number of groups are pursuing numerical calculations and investigating possible systematic uncertainties. One systematic that has…