The role of the slope of `realistic' potential barriers in preventing relativistic tunnelling in the Klein zone

The transmission of fermions of mass m and energy E through an electrostatic potential barrier of rectangular shape (i.e. supporting an infinite electric field), of height U> E + m - due to the many-body nature of the Dirac equation evidentiated by the Klein paradox - has been widely studied. We exploit here the analytical solution, given by Sauter for the linearly rising potential step, to show that the tunnelling rate through a more realistic trapezoidal barrier is exponentially depressed, as soon as the length of the regions supporting a finite electric field exceeds the Compton wavelenght of the particle - the latter circumstance being hardly escapable in most realistic cases

Infra-Red Asymptotic Dynamics of Gauge Invariant Charged Fields: QED versus QCD

The freedom one has in constructing locally gauge invariant charged fields in gauge theories is analyzed in full detail and exploited to construct, in QED, an electron field whose two-point function W(p), up to the fourth order in the coupling constant, is normalized with on-shell normalization conditions and is, nonetheless, infra-red finite; as a consequence the radiative corrections vanish on the mass shell $p^2=\mu^2$ and the free field singularity is dominant, although, in contrast to quantum field theories with mass gap, the eigenvalue $\mu^2$ of the mass operator is not isolated. The same construction, carried out for the quark in QCD, is not sufficient for cancellation of infra-red divergences to take place in the fourth order. The latter divergences, however, satisfy a simple factorization equation. We speculate on the scenario that could be drawn about infra-red asymptotic dynamics of QCD, should this factorization equation be true in any order of perturbation theory.Comment: 30 pages, RevTex, 8 figures included using graphic

Charge density and electric charge in quantum electrodynamics

The convergence of integrals over charge densities is discussed in relation with the problem of electric charge and (non-local) charged states in Quantum Electrodynamics (QED). Delicate, but physically relevant, mathematical points like the domain dependence of local charges as quadratic forms and the time smearing needed for strong convergence of integrals of charge densities are analyzed. The results are applied to QED and the choice of time smearing is shown to be crucial for the removal of vacuum polarization effects responible for the time dependence of the charge (Swieca phenomenon). The possibility of constructing physical charged states in the Feynman-Gupta-Bleuler gauge as limits of local states vectors is discussed, compatibly with the vanishing of the Gauss charge on local states. A modification by a gauge term of the Dirac exponential factor which yields the physical Coulomb fields from the Feynman-Gupta-Bleuler fields is shown to remove the infrared divergence of scalar products of local and physical charged states, allowing for a construction of physical charged fields with well defined correlation functions with local fields

How equal is equality? Discussions about same-sex marriage in Portugal

In Portugal, public and political discussions about same-sex marriage have been going on since the 1990s. In 2010, same-sex marriage was legalized under intense dispute since it excludes same-sex couples from adoption and reproductive rights. During parliamentary debates, political parties and civil organizations linked to the Catholic Church resorted to conflicting ideas of ‘equality’ and ‘difference’ to advance their claims. In this article, we analyse the contents of petitions, bills and parliamentary proceedings concerning the legal recognition of same-sex unions, highlighting the presence of conflicting notions of equality linked to pervasive beliefs about the inadequacy of homo-erotic desire and practices

Charges in Gauge Theories

In this article we investigate charged particles in gauge theories. After reviewing the physical and theoretical problems, a method to construct charged particles is presented. Explicit solutions are found in the Abelian theory and a physical interpretation is given. These solutions and our interpretation of these variables as the true degrees of freedom for charged particles, are then tested in the perturbative domain and are demonstrated to yield infra-red finite, on-shell Green's functions at all orders of perturbation theory. The extension to collinear divergences is studied and it is shown that this method applies to the case of massless charged particles. The application of these constructions to the charged sectors of the standard model is reviewed and we conclude with a discussion of the successes achieved so far in this programme and a list of open questions.Comment: 47 pages, LaTeX, 14 figures, uses feynmp, necessary Metapost files included. Review to appear in Pramana, Journal of Physics. Minor LaTeX change to make page numbers visible on "Letter" paper forma

Negotiating queer and religious identities in higher education: queering ‘progression’ in the ‘university experience’

This article addresses the negotiation of ‘queer religious’ student identities in UK higher education. The ‘university experience’ has generally been characterised as a period of intense transformation and self-exploration, with complex and overlapping personal and social influences significantly shaping educational spaces, subjects and subjectivities. Engaging with ideas about progressive tolerance and becoming, often contrasted against ‘backwards’ religious homophobia as a sentiment/space/subject ‘outside’ education, this article follows the experiences and expectations of queer Christian students. In asking whether notions of ‘queering higher education’ (Rumens 2014 Rumens, N. 2014. “Queer Business: Towards Queering the Purpose of the Business School.” In The Entrepreneurial University: Public Engagements, Intersecting Impacts, edited by Y. Taylor, 82–104. Basingstoke: Palgrave Macmillan.) ‘fit’ with queer-identifying religious youth, the article explores how educational experiences are narrated and made sense of as ‘progressive’. Educational transitions allow (some) sexual-religious subjects to negotiate identities more freely, albeit with ongoing constraints. Yet perceptions of what, where and who is deemed ‘progressive’ and ‘backwards’ with regard to sexuality and religion need to be met with caution, where the ‘university experience’ can shape and shake sexual-religious identity

Integrated Indicators for the Estimation of Vulnerability to Land Degradation

In this chapter we approach the assessment of the vulnerability to land degradation of a typical Mediterranean environment using a modified version of the ESA model. This approach combines analyses of the socio-economic component with analyses of the vegetation trends. According to the standard ESA strategy, different indicators representing the impact of agricultural and grazing activities are used. The main feature of these indicators is that they are census-based and consequently suitable only for the analysis at municipal scale. Therefore we have also elaborated a mechanization index (proxy for soil compaction induced by agricultural machineries) that uses land cover and morphological data [36], enabling high spatial resolution and faster rate of update. The indicators related to the anthropic impact are integrated into an overall Land Management Index (LMI) and in each area it is possible to enhance the main contributing factors to highlight the prevailing forces that drive human-induced degradation processes. In order to include vegetation in the vulnerability map we analyze satellite vegetation index NDVI (Normalized Difference Vegetation Index) which is recognized as ideal tool for monitoring long term trends of degradation phenomena and assessing different values of severity of the concerned processes [37,38]. The final result of our analyses is an integrated vulnerability map of the investigated region, accounting for management and vegetation factors, which allows us to identify priority sites where restoration/rehabilitation interventions are urgent. The adopted procedure can be easily applied to geographic contexts characterized by high complexity in terms of land cover type and economic vocation (intensive agriculture, grazing, industrial activities) thus enabling an early detection of the areas most vulnerable to land degradation

An Organizational Model of a Food Production Chain: A Case Study in the Poultry Sector in Foggia (Italy)

The purpose of this study was to analyze the poultry chain in southern Italy to describe the characteristics of farms and their locations and to propose an optimized organizational model with a broader approach that considers not only economic and environmental factors, but also ethical ones, including animal welfare protection, particularly in the poultry food safety chain. To obtain these results, the geolocations of poultry facilities, identifying possible verticalizations in the supply chain, were used. Data were collected in the province of Foggia (Italy) and organized in a dataset in collaboration with the Prevention Department of the Local Health Authority. A geo-imputation procedure and centroid calculation allowed us to formulate an optimizing hypothesis regarding the geolocation of upstream and downstream facilities in the process of chicken breeding by identifying a possible verticalization in the supply chain. Our results highlight the importance of broadening the concept of industrial symbiosis in the management of poultry farming, not only from an environmental perspective, but also from a social perspective. In particular, concerning ethical aspects, protecting animal welfare today is an essential goal of the sector to ensure high quality and yield of poultry meat. The results represent the first step towards proposing an optimized organizational model that takes ethical and social aspects into consideration. The paper is intended to highlight how, in the poultry sector, an organizational scheme can also reconcile other aspects, such as safeguarding the welfare conditions of animals on farms and during transport to improve food safety. © 2025 by the authors