Related papers: Quantum gravity and the Coulomb potential
The Schr\"odinger equations for the Coulomb and the Harmonic oscillator potentials are solved in the cosmic-string conical space-time. The spherical harmonics with angular deficit are introduced. The algebraic construction of the harmonic…
Based on the observation that the exterior space-times of Schwarzschild-type solutions allow two symmetric slicings, a static spherically symmetric one and a timelike homogeneous one, modifications of gravitational dynamics suggested by…
The physical interpretation and eventual fate of gravitational singularities in a theory surpassing classical general relativity are puzzling questions that have generated a great deal of interest among various quantum gravity approaches.…
Besides the standard quantum version of the Coulomb/Kepler problem, an alternative quantum model with not too dissimilar phenomenological (i.e., spectral and scattering) as well as mathematical (i.e., exact-solvability) properties may be…
We study a relativistic quantum particle in cosmic string spacetime in the presence of a uniform magnetic field and a Coulomb-type scalar potential. It is shown that the radial part of this problem possesses the $su(1,1)$ symmetry. We…
The problem of finding the quantum theory of the gravitational field, and thus understanding what is quantum spacetime, is still open. One of the most active of the current approaches is loop quantum gravity. Loop quantum gravity is a…
Deviations from the uniform oscillator spacing, related to the shape of the confining potential, have a strong influence on few-electron states in quantum dots when Coulomb effects are included. Distinct signatures are found for level…
The framework of quantum symmetry reduction is applied to loop quantum gravity with respect to transitively acting symmetry groups. This allows to test loop quantum gravity in a large class of minisuperspaces and to investigate its features…
We consider a spacetime singularity at $t = 0$ arising in a Kasner-type metric that solves the gravitational equations modified by quantum effects of a conformal field theory (CFT). The resulting constraints can be solved efficiently when…
Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…
We calculate exactly, using finite size techniques, the quantum mechanical and many-body effects to the self-capacitance of a spherical quantum dot in the regime of extreme confinement, where the radius of the sphere is much smaller than…
A manifestly Lorentz-covariant formulation of Loop Quantum Gravity (LQG) is given in terms of finite-dimensional representations of the Lorentz group. The formulation accounts for discrete symmetries, such as parity and time-reversal, and…
We present an implementation of the loop representation of quantum gravity on a square lattice. Instead of starting from a classical lattice theory, quantizing and introducing loops, we proceed backwards, setting up constraints in the…
Quantum gravity is expected to be necessary in order to understand situations where classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e. the fact that the backward evolution…
We study numerically the effects of loop quantum gravity motivated corrections on massless scalar field collapse in Painlev\'e-Gullstrand coordinates. Near criticality, the system exhibits Choptuik scaling with the added features of a mass…
The behaviour of a relativistic scalar particle in a possible scenario that arises from the violation of the Lorentz symmetry is investigated. The background of the Lorentz symmetry violation is defined by a tensor field that governs the…
We quantize an inhomogeneous cosmological model using techniques that include polymeric quantization. More explicitly, we construct well defined operators to represent the constraints and find the physical Hilbert space formed by their…
We study the quantum mechanics of self-gravitating thin shell collapse by solving the polymerized Wheeler-DeWitt equation. We obtain the energy spectrum and solve the time dependent equation using numerics. In contradistinction to the…
In recent twenty years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. We consider the quantum dynamics of a real massless scalar field coupled to…
Polymer models are effective in describing quantum gravity effects around the initial singularity, leading to its replacement by bouncing surfaces on which the curvature and densities are finite. Their properties depend on the space-time…