On the geometry of quantum indistinguishability

An algebraic approach to the study of quantum mechanics on configuration spaces with a finite fundamental group is presented. It uses, in an essential way, the Gelfand-Naimark and Serre-Swan equivalences and thus allows one to represent geometric properties of such systems in algebraic terms. As an application, the problem of quantum indistinguishability is reformulated in the light of the proposed approach. Previous attempts aiming at a proof of the spin-statistics theorem in non-relativistic quantum mechanics are explicitly recast in the global language inherent to the presented techniques. This leads to a critical discussion of single-valuedness of wave functions for systems of indistinguishable particles. Potential applications of the methods presented in this paper to problems related to quantization, geometric phases and phase transitions in spin systems are proposed.Comment: 24 page

Fermion Quasi-Spherical Harmonics

Spherical Harmonics, $Y_\ell^m(\theta,\phi)$, are derived and presented (in a Table) for half-odd-integer values of $\ell$ and $m$. These functions are eigenfunctions of $L^2$ and $L_z$ written as differential operators in the spherical-polar angles, $\theta$ and $\phi$. The Fermion Spherical Harmonics are a new, scalar and angular-coordinate-dependent representation of fermion spin angular momentum. They have $4\pi$ symmetry in the angle $\phi$, and hence are not single-valued functions on the Euclidean unit sphere; they are double-valued functions on the sphere, or alternatively are interpreted as having a double-sphere as their domain.Comment: 16 pages, 2 Tables. Submitted to J.Phys.

A setting for higher order differential equations fields and higher order Lagrange and Finsler spaces

We use the Fr\"olicher-Nijenhuis formalism to reformulate the inverse problem of the calculus of variations for a system of differential equations of order 2k in terms of a semi-basic 1-form of order k. Within this general context, we use the homogeneity proposed by Crampin and Saunders in [14] to formulate and discuss the projective metrizability problem for higher order differential equation fields. We provide necessary and sufficient conditions for higher order projectivpre-e metrizability in terms of homogeneous semi-basic 1-forms. Such a semi-basic 1-form is the Poincar\'e-Cartan 1-form of a higher order Finsler function, while the potential of such semi-basic 1-form is a higher order Finsler function.Comment: final, pre-published versio

First-Principles Dynamical Coherent-Potential Approximation Approach to the Ferromagnetism of Fe, Co, and Ni

Magnetic properties of Fe, Co, and Ni at finite temperatures have been investigated on the basis of the first-principles dynamical CPA (Coherent Potential Approximation) combined with the LDA (Local Density Approximation) + $U$ Hamiltonian in the Tight-Binding Linear Muffintin Orbital (TB-LMTO) representation. The Hamiltonian includes the transverse spin fluctuation terms. Numerical calculations have been performed within the harmonic approximation with 4th-order dynamical corrections. Calculated single-particle densities of states in the ferromagnetic state indicate that the dynamical effects reduce the exchange splitting, suppress the band width of the quasi-particle state, and causes incoherent excitations corresponding the 6 eV satellites. Results of the magnetization vs temperature curves, paramagnetic spin susceptibilities, and the amplitudes of local moments are presented. Calculated Curie temperatures ($T_{\rm C}$) are reported to be 1930K for Fe, 2550K for Co, and 620K for Ni; $T_{\rm C}$ for Fe and Co are overestimated by a factor of 1.8, while $T_{\rm C}$ in Ni agrees with the experimental result. Effective Bohr magneton numbers calculated from the inverse susceptibilities are 3.0 $\mu_{\rm B}$ (Fe), 3.0 $\mu_{\rm B}$ (Co), and 1.6 $\mu_{\rm B}$ (Ni), being in agreement with the experimental ones. Overestimate of $T_{\rm C}$ in Fe and Co is attributed to the neglects of the higher-order dynamical effects as well as the magnetic short range order.Comment: 10 pages, 13 figure

Notes on the Third Law of Thermodynamics.I

We analyze some aspects of the third law of thermodynamics. We first review both the entropic version (N) and the unattainability version (U) and the relation occurring between them. Then, we heuristically interpret (N) as a continuity boundary condition for thermodynamics at the boundary T=0 of the thermodynamic domain. On a rigorous mathematical footing, we discuss the third law both in Carath\'eodory's approach and in Gibbs' one. Carath\'eodory's approach is fundamental in order to understand the nature of the surface T=0. In fact, in this approach, under suitable mathematical conditions, T=0 appears as a leaf of the foliation of the thermodynamic manifold associated with the non-singular integrable Pfaffian form $\delta Q_{rev}$. Being a leaf, it cannot intersect any other leaf $S=$ const. of the foliation. We show that (N) is equivalent to the requirement that T=0 is a leaf. In Gibbs' approach, the peculiar nature of T=0 appears to be less evident because the existence of the entropy is a postulate; nevertheless, it is still possible to conclude that the lowest value of the entropy has to belong to the boundary of the convex set where the function is defined.Comment: 29 pages, 2 figures; RevTex fil

Gravitational Lensing

Gravitational lensing has developed into one of the most powerful tools for the analysis of the dark universe. This review summarises the theory of gravitational lensing, its main current applications and representative results achieved so far. It has two parts. In the first, starting from the equation of geodesic deviation, the equations of thin and extended gravitational lensing are derived. In the second, gravitational lensing by stars and planets, galaxies, galaxy clusters and large-scale structures is discussed and summarised.Comment: Invited review article to appear in Classical and Quantum Gravity, 85 pages, 15 figure

Integrating Values, Purposes, and Visions for Responsible Development

This chapter highlights a study showing that knowledge sharing and envisioning processes can have positive effects on human and social capital growth within a network. The chapter begins by arguing that a responsible development perspective can be more proactive approach than a sustainability perspective. Some actors (non-profit, public, and private) have achieved responsible development goals by integrating values, purposes and visions. More specifically, we conducted a study testing a methodology that can guide a process of building a strategic vision within a network with the goal of improving their responsible development orientation. The chosen methodology is “Participatory Action Research”. The implementation of the envisioning process was studied via quantitative/qualitative research tools. The methodology was tested in an official cross-country project funded by the European Commission. The project was selected as a best practice by the same European Union Commission. The study highlights the importance of envisioning processes in building social and human capital at the inter-organizational level and, in particular, in highly complex sectors such as those oriented towards improving social responsibility. In fact, work on the envisioning process itself represents an essential instrument for developing strategic objectives to be shared among actors within networks that intend to promote responsible development and improve their human and social capital. This bottom-up process of envisioning can also facilitate cultural interaction among community members, even in a cross-country context. This relevant “learning-by-interacting” experience, can create a growth process for the human and social capital of entire communities. The creation of social capital also promotes the development of shared knowledge and advances leading to the general understanding of common core objectives and appropriate ways of acting within the social system. The chapter ends with recommendations for future research

Impact of Chronic Lung Disease on Very Low Birth Weight infants: a collaborative study of the Italian Group of Neonatal Pneumology

Objective. To evaluate the incidence and risk factors for chronic lung disease in a population of very low birth weight infants. Methods. In a prospective multicentric trial all very low birth weight infants (< 1500 g) accepted in 36 Italian Neonatal Intensive care units were studied from February 89 to January 99. For each patient were recorded maternal history, perinatal events, respiratory disease, infections, patent ductus arteriosus, retinopathy of prematurity, intraventricular haemorrhage and final outcome. Logistic regression analysis was performed in a multivariate assessment of risk factors for chronic lung disease. Results. In the study were included 1634 patients: 1387 infants survived beyond 36 weeks and 6.9% of them still oxygen dependent. The incidence of chronic lung disease was higher among babies with a gestational age of < 28 weeks and weight \ub2 1000 g. The multivariate analysis showed that low birth weight, respiratory distress syndrome, persistent ductus arteriosus and sepsis were the main risk factors. Conclusions. In our study the incidence of chronic lung disease was relatively lo

A Model for the Development of the Rhizobial and Arbuscular Mycorrhizal Symbioses in Legumes and Its Use to Understand the Roles of Ethylene in the Establishment of these two Symbioses

We propose a model depicting the development of nodulation and arbuscular mycorrhizae. Both processes are dissected into many steps, using Pisum sativum L. nodulation mutants as a guideline. For nodulation, we distinguish two main developmental programs, one epidermal and one cortical. Whereas Nod factors alone affect the cortical program, bacteria are required to trigger the epidermal events. We propose that the two programs of the rhizobial symbiosis evolved separately and that, over time, they came to function together. The distinction between these two programs does not exist for arbuscular mycorrhizae development despite events occurring in both root tissues. Mutations that affect both symbioses are restricted to the epidermal program. We propose here sites of action and potential roles for ethylene during the formation of the two symbioses with a specific hypothesis for nodule organogenesis. Assuming the epidermis does not make ethylene, the microsymbionts probably first encounter a regulatory level of ethylene at the epidermis–outermost cortical cell layer interface. Depending on the hormone concentrations there, infection will either progress or be blocked. In the former case, ethylene affects the cortex cytoskeleton, allowing reorganization that facilitates infection; in the latter case, ethylene acts on several enzymes that interfere with infection thread growth, causing it to abort. Throughout this review, the difficulty of generalizing the roles of ethylene is emphasized and numerous examples are given to demonstrate the diversity that exists in plants

Hidden husbandry: disentangling a disturbed profile at Beckery Chapel, a medieval ecclesiastical site near Glastonbury (UK)

Beckery Chapel, near Glastonbury, is the site which has the earliest scientific dating evidence for monastic life in the UK, and later in the medieval period became a Chapel that played a significant role as a destination for pilgrims, as part of the Glastonbury Abbey estate. The site was previously excavated in the 1880s and the 1960s, and in 2016 the South West Heritage Trust excavated a building, that proved to be an outbuilding used when the medieval chapel was in operation. Soil micromorphological analysis was conducted first to understand the sediments within the profile from this building, which appeared fairly homogenous and bioturbated in the field. It untangled the bioturbation processes and revealed a rare northern European, geoarchaeological example of a livestock enclosure from a dryland context in this temperate environment. The results of our innovative multi-proxy approach highlight the potential and methodological considerations for future studies to integrate micromorphology, palaeoparasitology and mycology to examine animal management on dryland archaeological sites. They increase the knowledge of the economic activities of the ecclesiastical occupation at Beckery, contributing to an enhanced understanding of the Chapel site, its wider landscape and its role as part of the Glastonbury Abbey estate