Integrability Criterion for Abelian Extensions of Lie Groups

We establish a criterion for when an abelian extension of infinite-dimensional Lie algebras integrates to a corresponding Lie group extension $\hat{G}$ of $G$ by $A$, where $G$ is a connected, simply connected Lie group and $A$ is a quotient of its Lie algebra by some discrete subgroup. When $G$ is non-simply connected, the kernel $A$ is replaced by a central extension $\hat{A}$ of $\pi_1(G)$ by $A$.Comment: 11 pages, 2 figure

Exact Ultra Cold Neutrons' Energy Spectrum in Gravitational Quantum Mechanics

We find exact energy eigenvalues and eigenfunctions of the quantum bouncer in the presence of the minimal length uncertainty and the maximal momentum. This form of Generalized (Gravitational) Uncertainty Principle (GUP) agrees with various theories of quantum gravity and predicts a minimal length uncertainty proportional to $\hbar\sqrt{\beta}$ and a maximal momentum proportional to $1/\sqrt{\beta}$, where $\beta$ is the deformation parameter. We also find the semiclassical energy spectrum and discuss the effects of this GUP on the transition rate of the ultra cold neutrons in gravitational spectrometers. Then, based on the Nesvizhevsky's famous experiment, we obtain an upper bound on the dimensionless GUP parameter.Comment: 11 pages, 1 figure, to appear in European Physical Journal

On the boundary conditions in deformed quantum mechanics with minimal length uncertainty

We find the coordinate space wave functions, maximal localization states, and quasiposition wave functions in a GUP framework that implies a minimal length uncertainty using a formally self-adjoint representation. We show that how the boundary conditions in quasiposition space can be exactly determined from the boundary conditions in coordinate space.Comment: 9 pages, to appear in Advances in High Energy Physic

Digital ethnography, resistance art and communication media in Iran

Iranian visual materials relating to the presidential election crisis have the potential to become the sites of analysis and debate for fields as diverse as history, visual history, memory and post-memory, or trauma studies. References to memory are now omnipresent in scholarly discourse and in a wider public debate: ”social memory’, “collective remembrance”, “national memory”, “public memory”, “counter memory”, “popular history making” and “lived history” jostle for attention.Publisher PDFPeer reviewe

Coherent States in Gravitational Quantum Mechanics

We present the coherent states of the harmonic oscillator in the framework of the generalized (gravitational) uncertainty principle (GUP). This form of GUP is consistent with various theories of quantum gravity such as string theory, loop quantum gravity, and black-hole physics and implies a minimal measurable length. Using a recently proposed formally self-adjoint representation, we find the GUP-corrected Hamiltonian as a generator of the generalized Heisenberg algebra. Then following Klauder's approach, we construct exact coherent states and obtain the corresponding normalization coefficients, weight functions, and probability distributions. We find the entropy of the system and show that it decreases in the presence of the minimal length. These results could shed light on possible detectable Planck-scale effects within recent experimental tests.Comment: 17 pages, 4 figures, to appear in Int. J. Mod. Phys.

A Higher Order GUP with Minimal Length Uncertainty and Maximal Momentum

We present a higher order generalized (gravitational) uncertainty principle (GUP) in the form $[X,P]=i\hbar/(1-\beta P^2)$. This form of GUP is consistent with various proposals of quantum gravity such as string theory, loop quantum gravity, doubly special relativity, and predicts both a minimal length uncertainty and a maximal observable momentum. We show that the presence of the maximal momentum results in an upper bound on the energy spectrum of the momentum eigenstates and the harmonic oscillator.Comment: 13 pages, 4 figure

A class of GUP solutions in deformed quantum mechanics

Various candidates of quantum gravity such as string theory, loop quantum gravity and black hole physics all predict the existence of a minimum observable length which modifies the Heisenberg uncertainty principle to so-called Generalized Uncertainty Principle (GUP). This approach results in the modification of the commutation relations and changes all Hamiltonians in quantum mechanics. In this paper, we present a class of physically acceptable solutions for a general commutation relation without directly solving the corresponding generalized Schrodinger equations. These solutions satisfy the boundary conditions and exhibit the effect of the deformed algebra on the energy spectrum. We show that, this procedure prevents us from doing equivalent but lengthy calculations.Comment: 9 pages, 1 figur

A note on the one-dimensional hydrogen atom with minimal length uncertainty

We present exact energy spectrum and eigenfunctions of the one-dimensional hydrogen atom in the presence of the minimal length uncertainty. By requiring the self-adjointness property of the Hamiltonian, we completely determine the quantization condition. We indicate that the single-valuedness criteria of the eigenfunctions in non-deformed case is an emergent condition and the semiclassical solutions exactly coincide with the quantum mechanical results. The behavior of the wave functions at the origin in coordinate space and in quasiposition space is discussed finally.Comment: 12 pages, to appear in Journal Physics A: Mathematical and Theoretica