Related papers: New volume and inverse volume operators for loop q…
The choice of mathematical representation when describing physical systems is of great consequence, and this choice is usually determined by the properties of the problem at hand. Here we examine the little-known wave operator…
A key problem in the attempt to quantize the gravitational field is the choice of boundary conditions. These are mixed, in that spatial and normal components of metric perturbations obey different sets of boundary conditions. In the…
We introduce a new operator in Loop Quantum Gravity - the 3D curvature operator - related to the 3-dimensional scalar curvature. The construction is based on Regge Calculus. We define it starting from the classical expression of the Regge…
We present a concise description of the basic features of gravity-matter models based on the formalism of non-canonical spacetime volume-forms in its two versions: the method of non-Riemannian volume-forms (metric-independent covariant…
In the context of Covariant Quantum Mechanics for a spin particle, we classify the ``quantum vector fields'', i.e. the projectable Hermitian vector fields of a complex bundle of complex dimension 2 over spacetime. Indeed, we prove that the…
We characterize the quasianti-Hermitian quaternionic operators in QQM by means of their spectra; moreover, we state a necessary and sufficient condition for a set of quasianti-Hermitian quaternionic operators to be anti-Hermitian with…
Although the cosmological perturbations with inverse-volume corrections from loop quantum cosmology have been studied using the anomaly-free algebra approach in much of the literature, there still remains an important issue that some…
Quantum gravity is made more difficult in part by its constraint structure. The constraints are classically first-class; however, upon quantization they become partially second-class. To study such behavior, we focus on a simple problem…
Degenerate geometrical configurations in quantum gravity are important to understand if the fate of classical singularities is to be revealed. However, not all degenerate configurations arise on an equal footing, and one must take into…
The leading quantum correction to Einstein-Hilbert Hamiltonian coming from large volume vacuum isotropic loop quantum cosmology, is independent of quantization ambiguity parameters. It is shown here that this correction can be viewed as…
A possible alternative route to a quantum theory of gravity is presented. The usual path is to quantize the gravitational field in order to introduce the statistical structure characteristic of quantum mechanics. The procedure followed here…
We propose a new type of gauge in two-dimensional quantum gravity. We investigate pure gravity in this gauge, and find that the system reduces to quantum mechanics of loop length $l$. Furthermore, we rederive the $c\!=\!0$ string field…
Effective equations are often useful to extract physical information from quantum theories without having to face all technical and conceptual difficulties. One can then describe aspects of the quantum system by equations of classical type,…
Time in relativity theory has a status different from that adopted by standard quantum mechanics, where time is considered as a parameter measured with reference to an external absolute Newtonian frame. This status strongly restricts its…
It has been discussed earlier that ( weak quasi-) quantum groups allow for conventional interpretation as internal symmetries in local quantum theory. From general arguments and explicit examples their consistency with (braid-) statistics…
We continue the semiclassical analysis of the Loop Quantum Gravity (LQG) volume operator that was started in the companion paper [23]. In the first paper we prepared the technical tools, in particular the use of complexifier coherent states…
The states of the physical algebra, namely the algebra generated by the operators involved in encoding and processing qubits, are considered instead of those of the whole system-algebra. If the physical algebra commutes with the interaction…
Quantum mechanics of a particle in an infinite square well under the influence of a time-dependent electric field is reconsidered. In some gauge, the Hamiltonian depends linearly on the momentum operator which is symmetric but not…
We consider non-local properties of quanternionic quantum mechanics, in which the complex numbers are replaced by the quaternions as the underlying algebra. Specifically, we show that it is possible to construct a non-local box. This allows…
We construct a Heisenberg-like algebra for the one dimensional infinite square-well potential in quantum mechanics. The ladder operators are realized in terms of physical operators of the system as in the harmonic oscillator algebra. These…