Comments on "Schwinger's Model of Angular Momentum with GUP" by H. Verma et al, arXiv:1808.00766

In this note, we show that the methodology and conclusions of "Schwinger's Model of Angular Momentum with GUP" [arxiv:1808.00766] are flawed and that the conclusions of "Generalized Uncertainty Principle and angular momentum" (P. Bosso and S. Das) [arxiv:1607.01083] remain valid.Comment: 3 page

Generalized Uncertainty Principle and Angular Momentum

Various models of quantum gravity suggest a modification of the Heisenberg's Uncertainty Principle, to the so-called Generalized Uncertainty Principle, between position and momentum. In this work we show how this modification influences the theory of angular momentum in Quantum Mechanics. In particular, we compute Planck scale corrections to angular momentum eigenvalues, the Hydrogen atom spectrum, the Stern-Gerlach experiment and the Clebsch-Gordan coefficients. We also examine effects of the Generalized Uncertainty Principle on multi-particle systems.Comment: 21 pages, 2 figures, minor revisions, to appear in Annals of Physic

Lorentz invariant mass and length scales

We show that the standard Lorentz transformations admit an invariant mass (length) scale, such as the Planck scale. In other words, the frame independence of such scale is built-in within those transformations, and one does not need to invoke the principle of relativity for their invariance. This automatically ensures the frame-independence of the spectrum of geometrical operators in quantum gravity. Furthermore, we show that the above predicts a small but measurable difference between the inertial and gravitational mass of any object, regardless of its size or whether it is elementary or composite.Comment: 10 page

Relativistic Generalized Uncertainty Principle

The Generalized Uncertainty Principle and the related minimum length are normally considered in non-relativistic Quantum Mechanics. Extending it to relativistic theories is important for having a Lorentz invariant minimum length and for testing the modified Heisenberg principle at high energies.In this paper, we formulate a relativistic Generalized Uncertainty Principle. We then use this to write the modified Klein-Gordon, Schr\"odinger and Dirac equations, and compute quantum gravity corrections to the relativistic hydrogen atom, particle in a box, and the linear harmonic oscillator.Comment: 6 pages, Revte

Rigorous Hamiltonian and Lagrangian analysis of classical and quantum theories with minimal length

GUP is a phenomenological model aimed for a description of a minimal length in quantum and classical systems. However, the analysis of problems in classical physics is usually approached preferring a different formalism than the one used for quantum systems, and vice versa. Potentially, the two approaches can result in inconsistencies. Here, we eliminate such inconsistencies proposing particular meanings and relations between the variables used to describe physical systems, resulting in a precise form of the Legendre transformation. Furthermore, we introduce two different sets of canonical variables and the relative map between them. These two sets allow for a complete and unambiguous description of classical and quantum systems.Comment: 15 pages, 4 figure

Long term effects of mesoglycan on brachial arterial stiffness and MMP-9/TIMP-1 system in patients with metabolic syndrome

Objectives: The aim of this study was to evaluate the chronic effects of mesoglycan on the vascular remodeling in patients with metabolic syndrome (Mets). Background: MetS is defined by a clustering of vascular risk factors that require both pharmacologic and non-pharmacologic interventions, including body weight reductions and physical activity. The correction of vascular remodeling associated with MetS has lately received increasing interest. Methods: Thirty consecutive ambulatory patients affected by MetS were 2:1 randomized in a doubleblind fashion to receive mesoglycan or placebo, respectively. At the beginning and after 90 days of oral treatment we appraised the effects of mesoglycan (50 mg per os bid) or placebo on vascular remodeling, as assessed by the measurement of arterial wall elastic properties. Moreover, the matrix metalloproteinase’s (MMPs) type 9 and tissue inhibitor of metalloproteinase (TIMP) type 1 were analyzed by enzyme-linked immune sorbent assay (ELISA) and gelatin substrate zymography at the beginning of the study and after 90 days of treatment. Results: After 90 days of treatment, a marked improvement of arterial distensibility and compliance was detected in Mesoglycan group, with associated significant reduction of arterial stiffness, and a significant reduction of serum levels of MMP-9 and TIMP-1 and significant reduction of enzyme activity of MMPs. Conclusions: This small, preliminary study shows that mesoglycan exerts relevant effects on vascular remodeling after three-month treatment, in patients affected by metabolic syndrome