Existence of a minimal measurable length and an upper bound for the momentum fluctuations are the casting reasons for generalization of uncertainty principle and then reformulation of Hilbert space representation of quantum mechanics. In this paper, we study the consequences of the Generalized Uncertainty Principle (GUP) in the presence of both minimal length and maximal momentum. We consider a simple harmonic oscillator in the framework of GUP by introducing it's energy eigenstates and energy spectrum. Investigation of coherent states for a generalized harmonic oscillator and it's generic behavior are the other topics in our study.
We consider the fourth-order differential theory of gravitation to treat the problem of singularity avoidance: studying the short-distance behaviour in the case of black-holes and the big-bang we are going to see a way to attack the issue from a general perspective.
We introduce a new family of coherent states for loop quantum gravity, inspired by the twisted geometry parametrization. We compute their peakedness properties and compare them with the heat-kernel coherent states. They show similar features for the area and the holonomy operators, but improved peakedness in the direction of the flux. At the gauge-invariant level, the new family is built from tensor products of coherent intertwiners. To study the peakedness of the holonomy operator, we introduce a new shift operator based on the harmonic oscillator representation associated with the twisted ge…
Although the dRGT massive gravity successfully explains the late-time cosmic acceleration, it cannot justify inflation. On the other hand, and in the frameworks of General Relativity and modified gravity, the interests and attempts to describe dark energy and inflation by using Lagranginas, which may have pole, have recently been enhanced. Subsequently, we are going to show that this kind of Lagrangian may justify inflation in the framework of dRGT massive gravity. The study is done focusing on the power and exponential potentials, and the results show a plausible consistency with the Planck 2…
We reconsider the status of the so-called second clock effect in Weyl gauge theories of gravity, which are invariant both under local Poincaré transformations and local changes of scale. In particular, we revisit and extend our previous demonstration that the second clock effect does not occur in such theories, in order both to clarify our argument and confirm our original findings in response to recent counterclaims in the literature.
Bridging Quantum and Semiclassical Volume: A Numerical Study of Coherent State Matrix Elements in Loop Quantum Gravity
School of Physics and Optoelectronics, South China University of Technology（华南理工大学物理与光电工程学院）；Institute for Theoretical Sciences and Department of Physics, Westlake University（西湖大学理论科学研究院和物理系）
We propose a new kind of coherent state for the general $SO(D+1)$ formulation of loop quantum gravity in the $(1+D)$-dimensional space-time. Instead of Thiemann's coherent state for $SO(D+1)$ gauge theory, our coherent spin-network state is given by constructing proper superposition over quantum numbers of the spin-networks with vertices labelled by the coherent intertwiners. Such superposition type coherent states are labelled by the so-called generalized twisted geometric variables which capture the geometric meaning of discretized general relativity. We study the basic properties of this ki…
In this paper, we study self-dual gravity in the Newman-Penrose formalism. We specify the self-dual solution space from the Newman-Unti solutions. We show that the asymptotic symmetries of the self-dual gravity are still the (extended) BMS symmetries. We transform the self-dual Taub-NUT solution into the Newman-Unti gauge in analytical form.
