Quaternionic Madelung Transformation and Non-Abelian Fluid Dynamics

In the 1920's, Madelung noticed that if the complex Schroedinger wavefunction is expressed in polar form, then its modulus squared and the gradient of its phase may be interpreted as the hydrodynamic density and velocity, respectively, of a compressible fluid. In this paper, we generalize Madelung's transformation to the quaternionic Schroedinger equation. The non-abelian nature of the full SU(2) gauge group of this equation leads to a richer, more intricate set of fluid equations than those arising from complex quantum mechanics. We begin by describing the quaternionic version of Madelung's transformation, and identifying its ``hydrodynamic'' variables. In order to find Hamiltonian equations of motion for these, we first develop the canonical Poisson bracket and Hamiltonian for the quaternionic Schroedinger equation, and then apply Madelung's transformation to derive non-canonical Poisson brackets yielding the desired equations of motion. These are a particularly natural set of equations for a non-abelian fluid, and differ from those obtained by Bistrovic et al. only by a global gauge transformation. Because we have obtained these equations by a transformation of the quaternionic Schroedinger equation, and because many techniques for simulating complex quantum mechanics generalize straightforwardly to the quaternionic case, our observation leads to simple algorithms for the computer simulation of non-abelian fluids.Comment: 15 page

Noncommuting fields and non-Abelian fluids

The original ideas about noncommuting coordinates are recalled. The connection between U(1) gauge fields defined on noncommuting coordinates and fluid mechanics is explained. Non-Abelian fluid mechanics is described.Comment: 16 pp., invited talk at "Renormalization Group and Anomalies in Gravity and Cosmology", Ouro Preto, Brazil, March 2003. Minor typos correcte

Connection of Depression and Bone Loss in Perimenopausal and Postmenopausal Women

Depression has been implicated as a possible risk factor for low bone mineral density (BMD). However, there is still no solid evidence that could connect these two different illnesses. This research examined the association between self-reported depression and low BMD in perimenopausal and postmenopausal women. This research screened 130 female patients who were 44 to 72 years old and registered at the densitometry clinic of KBC Rijeka during a three month period. Densitometry was performed in order to establish their BMD and according to the results two groups of participants were formed: normal BMD – 38 participants with normal BMD at hip and spine and reduced BMD – 75 participants with lower BMD at hip and spine. Depression was assessed using Beck depression inventory. Both groups of participants were compared regarding their depression scores. There were no significant differences between the groups with normal and reduced BMD regarding mean age, age of menopause, length of menopause and number of births (p=0.001). Difference regarding depressiveness between the two groups was not significant (t=0.73; p=0.468). Also, there were no differences between the groups regarding the frequency of certain levels of depression. (c2=2.27; p=0.52). Results of this research suggest that self-reported depression is not associated with low BMD in perimenopausal and postmenopausal women

U(1) Gauge Theory as Quantum Hydrodynamics

It is shown that gauge theories are most naturally studied via a polar decomposition of the field variable. Gauge transformations may be viewed as those that leave the density invariant but change the phase variable by additive amounts. The path integral approach is used to compute the partition function. When gauge fields are included, the constraint brought about by gauge invariance simply means an appropriate linear combination of the gradients of the phase variable and the gauge field is invariant. No gauge fixing is needed in this approach that is closest to the spirit of the gauge principle. We derive an exact formula for the condensate fraction and in case it is zero, an exact formula for the anomalous exponent. We also derive a formula for the vortex strength which involves computing radiation corrections.Comment: 15 pages, Plain LaTeX, final published versio

Biopolymer‐based Carriers for DNA Vaccine Design

Abstract: Over the last 30 years, genetically engineered DNA has been tested as novel vaccination strategy against various diseases, including human immunodeficiency virus (HIV), hepatitis B, several parasites, and cancers. However, the clinical breakthrough of the technique is confined by the low transfection efficacy and immunogenicity of the employed vaccines. Therefore, carrier materials were designed to prevent the rapid degradation and systemic clearance of DNA in the body. In this context, biopolymers are a particularly promising DNA vaccine carrier platform due to their beneficial biochemical and physical characteristics, including biocompatibility, stability, and low toxicity. This article reviews the applications, fabrication, and modification of biopolymers as carrier medium for genetic vaccines

Metafluid dynamics and Hamilton-Jacobi formalism

Metafluid dynamics was investigated within Hamilton-Jacobi formalism and the existence of the hidden gauge symmetry was analyzed. The obtained results are in agreement with those of Faddeev-Jackiw approach.Comment: 7 page