On the geometry of the spin-statistics connection in quantum mechanics

The Spin-Statistics theorem states that the statistics of a system of identical particles is determined by their spin: Particles of integer spin are Bosons (i.e. obey Bose-Einstein statistics), whereas particles of half-integer spin are Fermions (i.e. obey Fermi-Dirac statistics). Since the original proof by Fierz and Pauli, it has been known that the connection between Spin and Statistics follows from the general principles of relativistic Quantum Field Theory. In spite of this, there are different approaches to Spin-Statistics and it is not clear whether the theorem holds under assumptions that are different, and even less restrictive, than the usual ones (e.g. Lorentz-covariance). Additionally, in Quantum Mechanics there is a deep relation between indistinguishabilty and the geometry of the configuration space. This is clearly illustrated by Gibbs' paradox. Therefore, for many years efforts have been made in order to find a geometric proof of the connection between Spin and Statistics. Recently, various proposals have been put forward, in which an attempt is made to derive the Spin-Statistics connection from assumptions different from the ones used in the relativistic, quantum field theoretic proofs. Among these, there is the one due to Berry and Robbins (BR), based on the postulation of a certain single-valuedness condition, that has caused a renewed interest in the problem. In the present thesis, we consider the problem of indistinguishability in Quantum Mechanics from a geometric-algebraic point of view. An approach is developed to study configuration spaces Q having a finite fundamental group, that allows us to describe different geometric structures of Q in terms of spaces of functions on the universal cover of Q. In particular, it is shown that the space of complex continuous functions over the universal cover of Q admits a decomposition into C(Q)-submodules, labelled by the irreducible representations of the fundamental group of Q, that can be interpreted as the spaces of sections of certain flat vector bundles over Q. With this technique, various results pertaining to the problem of quantum indistinguishability are reproduced in a clear and systematic way. Our method is also used in order to give a global formulation of the BR construction. As a result of this analysis, it is found that the single-valuedness condition of BR is inconsistent. Additionally, a proposal aiming at establishing the Fermi-Bose alternative, within our approach, is made.

Deep geometry of subduction below the Andean belt of Colombia as revealed by seismic tomography

In this study new tomographic models of Colombia were calculated. I used the seismicity recorded by the Colombian seismic network during the period 2006-2009. In this time period, the improvement of the seismic network yields more stable hypocentral results with respect to older data set and allows to compute new 3D Vp and Vp/Vs models. The final dataset consists of 10813 P- and 8614 S-arrival times associated to 1405 earthquakes. Tests with synthetic data and resolution analysis indicate that velocity models are well constrained in central, western and southwestern Colombia to a depth of 160 km; the resolution is poor in the northern Colombia and close to Venezuela due to a lack of seismic stations and seismicity. The tomographic models and the relocated seismicity indicate the existence of E-SE subducting Nazca lithosphere beneath central and southern Colombia. The North-South changes in Wadati-Benioff zone, Vp & Vp/Vs pattern and volcanism, show that the downgoing plate is segmented by slab tears E-W directed, suggesting the presence of three sectors. Earthquakes in the northernmost sector represent most of the Colombian seimicity and concentrated on 100-170 km depth interval, beneath the Eastern Cordillera. Here a massive dehydration is inferred, resulting from a delay in the eclogitization of a thickened oceanic crust in a flat-subduction geometry. In this sector a cluster of intermediate-depth seismicity (Bucaramanga Nest) is present beneath the elbow of the Eastern Cordillera, interpreted as the result of massive and highly localized dehydration phenomenon caused by a hyper-hydrous oceanic crust. The central and southern sectors, although different in Vp pattern show, conversely, a continuous, steep and more homogeneous Wadati-Benioff zone with overlying volcanic areas. Here a "normalthickened" oceanic crust is inferred, allowing for a gradual and continuous metamorphic reactions to take place with depth, enabling the fluid migration towards the mantle wedge.

Geometry of BV quantization and Mathai-Quillen formalism

Il formalismo Mathai-Quillen (MQ) è un metodo per costruire la classe di Thom di un fibrato vettoriale attraverso una forma differenziale di profilo Gaussiano. Lo scopo di questa tesi è quello di formulare una nuova rappresentazione della classe di Thom usando aspetti geometrici della quantizzazione Batalin-Vilkovisky (BV). Nella prima parte del lavoro vengono riassunti i formalismi BV e MQ entrambi nel caso finito dimensionale. Infine sfrutteremo la trasformata di Fourier “odd" considerando la forma MQ come una funzione definita su un opportuno spazio graduato.

The geometry of Lagrangian fibres

If the generic fibre f−1(c) of a Lagrangian fibration f : X → B on a complex Poisson– variety X is smooth, compact, and connected, it is isomorphic to the compactification of a complex abelian Lie–group. For affine Lagrangian fibres it is not clear what the structure of the fibre is. Adler and van Moerbeke developed a strategy to prove that the generic fibre of a Lagrangian fibration is isomorphic to the affine part of an abelian variety.rnWe extend their strategy to verify that the generic fibre of a given Lagrangian fibration is the affine part of a (C∗)r–extension of an abelian variety. This strategy turned out to be successful for all examples we studied. Additionally we studied examples of Lagrangian fibrations that have the affine part of a ramified cyclic cover of an abelian variety as generic fibre. We obtained an embedding in a Lagrangian fibration that has the affine part of a C∗–extension of an abelian variety as generic fibre. This embedding is not an embedding in the category of Lagrangian fibrations. The C∗–quotient of the new Lagrangian fibration defines in a natural way a deformation of the cyclic quotient of the original Lagrangian fibration.

Estrogen receptor- but not - or GPER inhibits high glucose-induced human VSMC proliferation: potential role of ROS and ERK

The decreased incidence of cardiovascular disease in premenopausal women has been attributed, at least partially, to protective effects of estrogens. However, premenopausal women with diabetes mellitus are no longer selectively protected. High-glucose (HG) conditions have previously been shown to abolish the antimitogenic effects of 17β-estradiol (E(2)) in vascular smooth muscle cells (VSMCs).

Operator variability using different polishing methods and surface geometry of a nanohybrid composite

This study evaluated the operator variability of different finishing and polishing techniques. After placing 120 composite restorations (Tetric EvoCeram) in plexiglassmolds, the surface of the specimens was roughened in a standardized manner. Twelve operators with different experience levels polished the specimens using the following finishing/polishing procedures: method 1 (40 ?m diamond [40D], 15 ?m diamond [15D], 42 ?m silicon carbide polisher [42S], 6 ?m silicon carbide polisher [6S] and Occlubrush [O]); method 2 (40D, 42S, 6S and O); method 3 (40D, 42S, 6S and PoGo); method 4 (40D, 42S and PoGo) and method 5 (40D, 42S and O). The mean surface roughness (Ra) was measured with a profilometer. Differences between the methods were analyzed with non-parametric ANOVA and pairwise Wilcoxon signed rank tests (?=0.05). All the restorations were qualitatively assessed using SEM. Methods 3 and 4 showed the best polishing results and method 5 demonstrated the poorest. Method 5 was also most dependent on the skills of the operator. Except for method 5, all of the tested procedures reached a clinically acceptable surface polish of Ra?0.2 ?m. Polishing procedures can be simplified without increasing variability between operators and without jeopardizing polishing results.

Neospora caninum and bone marrow-derived dendritic cells: parasite survival, proliferation, and induction of cytokine expression

Dendritic cells (DCs) represent the first line defence of the innate immune system following infection with pathogens. We exploratively addressed invasion and survival ability of Neospora caninum, a parasite causing abortion in cattle, in mouse bone marrow DCs (BMDCs), and respective cytokine expression patterns. Immature BMDCs were exposed to viable (untreated) and nonviable parasites that had been inactivated by different means. Invasion and/or internalization, as well as intracellular survival and proliferation of tachyzoites were determined by NcGRA2-RT-PCR and transmission electron microscopy (TEM). Cytokine expression was evaluated by reverse transcription (RT)-PCR and cytokine ELISA. Transmission electron microscopy of DCs stimulated with untreated viable parasites revealed that N. caninum was able to invade and proliferate within BMDCs. This was confirmed by NcGRA2-RT-PCR. On the other hand, no viable parasite organisms were revealed by TEM when exposing BMDCs to inactivated parasites (nonviability demonstrated by NcGRA2-RT-PCR). Cytokine expression analysis (as assessed by both RT-PCR and ELISA) demonstrated that both viable and nonviable parasites stimulated mBMDCs to express IL-12p40, IL-10 and TNF-alpha, whereas IL-4 RNA expression was not detected. Thus, exposure of mBMDCs to both viable and nonviable parasites results in the expression of cytokines that are relevant for a mixed Th1/Th2 immune response.

Rotational integral geometry of tensor valuations

We derive a new rotational Crofton formula for Minkowski tensors. In special cases, this formula gives (1) the rotational average of Minkowski tensors defined on linear subspaces and (2) the functional defined on linear subspaces with rotational average equal to a Minkowski tensor. Earlier results obtained for intrinsic volumes appear now as special cases.

Mechanisms of liposomal all-{\it trans\/} retinoic acid and vitamin D3 induced inhibition of cell proliferation and stimulation of apoptosis in aggressive B-cell non-Hodgkin's lymphoma

The Non-Hodgkin's Lymphoma (NHLs) are neoplasms of the immune system. Currently, less than 1% of the etiology of the 22,000 newly diagnosed lymphoma cases in the U.S.A. every year is known. This disease has a significant prevalence and high mortality rate. Cell growth in lymphomas has been shown to be an important parameter in aggressive NHL when establishing prognosis, as well as an integral part in the pathophysiology of the disease process. While many aggressive B cell NHLs respond initially to chemotherapeutic regimens such as CHOP-bleo (adriamycin, vincristine and bleomycin) etc., relapse is common, and the patient is then often refractory to further salvage treatment regimens.^ To assess their potential to inhibit aggressive B cell NHLs and induce apoptosis (also referred to as programmed cell death (PCD)), it was proposed to utilize the following biological agents-liposomal all-trans retinoic acid (L-ATRA) which is a derivative of Vitamin A in liposomes and Vitamin D3. Preliminary evidence indicates that L-ATRA may inhibit cell growth in these cells and may induce PCD as well. Detailed studies were performed to understand the above phenomena by L-ATRA and Vitamin D3 in recently established NHL-B cell lines and primary cell cultures. The gene regulation involved in the case of L-ATRA was also delineated. ^