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

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

Improving the Physical Exam with Technology - Point of Care Ultrasound

Point of Care Ultrasound is rapidly becoming standard of care for utilization in real time medical diagnostics and decision making. As such we sought to introduce ultrasound to medical students beginning in their first year and specifically incorporating it to mirror their physical exam teaching in the Practice of Clinical Medicine (PCM) course to help strengthen both their learning of the physical exam while also better understanding the utility of ultrasound use at the bedside. We sought to see if this strategy would result in improved examination scores via testing during their required objective structured clinical examination (OSCE) in the PCM course

Preparing a Better Doctor: the C3 curriculum and OSCE scores

In 2013, a horizontally integrated 18 month curriculum (C3) for undergraduate medical students, which replaced the traditional 24 month basic sciences curriculum, was implemented at the Virginia Commonwealth University School of Medicine. A retrospective, all-inclusive study was conducted comparing the performance of the last group of students completing the 24 month curriculum (the Class of 2016, n=196) and the first group of students completing the 18 month curriculum (the Class of 2017, n=205) on the end-of-course OSCE (Objective Structured Clinical Exam). Students who completed the 18 month curriculum had significantly higher OSCE case scores (7.7 points, p \u3c0.0001) as well as higher OSCE category scores (2.2 points, p = 0.002)

A Higher Order GUP with Minimal Length Uncertainty and Maximal Momentum II: Applications

In a recent paper, we presented a nonperturbative higher order generalized uncertainty principle (GUP) that 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. In this Letter, we find exact maximally localized states and present a formally self-adjoint and naturally perturbative representation of this modified algebra. Then we extend this GUP to D dimensions that will be shown it is noncommutative and find invariant density of states. We show that the presence of the maximal momentum results in upper bounds on the energy spectrum of the free particle and the particle in box. Moreover, this form of GUP modifies blackbody radiation spectrum at high frequencies and predicts a finite cosmological constant. Although it does not solve the cosmological constant problem, it gives a better estimation with respect to the presence of just the minimal length.Comment: 15 pages, 3 figures, second part of arXiv:1110.2999, to appear in Physics Letters

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