Classical Mechanics in Hilbert Space, Part 1

We consider the Hamilton formulation as well as the Hamiltonian flows on a symplectic (phase) space. These symplectic spaces are derivable from the Lie group of symmetries of the physical system considered. In Part 2 of this work, we then obtain the Hamiltonian formalism in the Hilbert spaces of square integrable functions on the symplectic spaces so obtained

Neumark Operators and Sharp Reconstructions, the finite dimensional case

A commutative POV measure $F$ with real spectrum is characterized by the existence of a PV measure $E$ (the sharp reconstruction of $F$) with real spectrum such that $F$ can be interpreted as a randomization of $E$. This paper focuses on the relationships between this characterization of commutative POV measures and Neumark's extension theorem. In particular, we show that in the finite dimensional case there exists a relation between the Neumark operator corresponding to the extension of $F$ and the sharp reconstruction of $F$. The relevance of this result to the theory of non-ideal quantum measurement and to the definition of unsharpness is analyzed.Comment: 37 page

Towards a realistic interpretation of quantum mechanics providing a model of the physical world

It is argued that a realistic interpretation of quantum mechanics is possible and useful. Current interpretations, from Copenhagen to many worlds are critically revisited. The difficulties for intuitive models of quantum physics are pointed out and possible solutions proposed. In particular the existence of discrete states, the quantum jumps, the alleged lack of objective properties, measurement theory, the probabilistic character of quantum physics, the wave-particle du- ality and the Bell inequalities are analyzed. The sketch of a realistic picture of the quantum world is presented. It rests upon the assump- tion that quantum mechanics is a stochastic theory whose randomness derives from the existence of vacuum fields. They correspond to the vacuum fluctuations of quantum field theory, but taken as real rather than virtual.Comment: 43 pages, paper throughout revised and somewhat enlarged, sections on the Bell inequalities and on the sketch of a picture of the quantum world rewritten, new references adde

Perspectives of 1H-NMR-based urinary metabonomics in fabry disease

High resolution proton magnetic resonance spectroscopy (1H-NMR) of body fluids coupled with multivariate data analysis has led to a new science known as metabonomics. Metabonomics is a powerful tool for investigating any disturbance in the normal homeostasis of biochemical processes. In particular, urine metabonomics provides information on the metabolite phenotype of the human being and is therefore appropriate to study the status of the global system. Here we applied 1H-NMR-based urinary metabonomics in a perspective study of the inherited lysosomal storage disorder known as Fabry disease, starting from the metabolite profiling of urine samples of male and female naïve Fabry subjects. Here we show that the 2 groups of patients can be fairly clearly separated into 2 classes due to statistically significant differences in the urinary level of some metabolites. This preliminary study shows that metabonomics can potentially be used for characterizing the biochemical mechanisms underlying the disease and, hopefully, for early diagnosis of Fabry disease. © 2010 Società Italiana di Nefrologia - ISSN 1121-8428

Microwave induced shift of the main phase transition in phosphatidylcholine membranes

Numerous experimental evidence show that exposure of biological systems to extremely high frequency microwaves may induce significant effects even at low powers. These effects are thought to occur via nonthermal mechanisms involving primarily the interaction of microwaves with phospholipid membrane structures. However, no conclusive experimental evidence that biomembranes exhibit remarkable sensitivity to this radiation has been provided up to now. Here, deuterium nuclear magnetic resonance spectroscopy is used to study the effects of microwaves on 1,2-Dimyristoyl-sn-glycero-3-phosphatidylcholine/2H2O multilamellar vesicles that serve as biomimetic membranes. Here we show that, if the membrane is brought into close proximity to the transition point, microwaves induce a reduction of water ordering at the membrane interface, an upward shift of the main phase transition temperature and a broadening of the transition region. A deep dosimetric analysis shows that the above effects are nonthermal, indicating the need for a nonthermal hypothesis to explain them. This study suggests that exposure to high-frequency microwaves can have far reaching consequences on active biological systems

Fabry disease: perspectives of urinary proteomics.

Fabry disease (FD) is an X-linked lysosomal storage disorder caused by mutations in the gene encoding the lysosomal enzyme a-galactosidase A (a-GalA). The resulting deficiency in a-GalA activity leads to intra-lysosomal accumulation of neutral glycosphingolipids, mainly globotriaosylceramide (Gb3), in various organ systems. As a consequence, a multisystem disorder develops, culminating in strokes and progressive renal and cardiac dysfunction. Enzyme replacement therapy (ERT) offers a specific treatment for patients affected by FD, though monitoring treatment is hampered by a lack of surrogate markers of response. Furthermore, even if signs and symptoms of the disease become manifest in childhood, its diagnosis is often delayed. Biomarkers that predict disease progression and respond relatively quickly to effective therapy may be useful to follow individual patients or groups of patients. Here we report the use of 2 different mass spectrometry-based proteomic techniques to identify disease-associated compositional changes that can be used as early biomarkers of the pathology, as well as for monitoring the effectiveness of ERT. To this purpose, we compared the renal Fabry urinary proteome with normal (control) urine using, respectively, 2-dimensional gel electrophoresis and label-free quantification. Our preliminary results show that the urinary protein pattern of affected patients can be easily distinguished from that of healthy subjects both qualitatively and quantitatively, thus encouraging further studies in the search for FD-specific biomarkers using this proteomic approac