Four Dimensional Quantum Yang-Mills Theory and Mass Gap

A quantization procedure for the Yang-Mills equations for the Minkowski space $\mathbf{R}^{1,3}$ is carried out in such a way that field maps satisfying Wightman axioms of Constructive Quantum Field Theory can be obtained. Moreover, by removing the ultra violet cut off, the spectrum of the corresponding QCD Hamilton operator is proven to be positive and bounded away from zero, except for the case of the vacuum state, which has vanishing energy level. The whole construction is gauge invariant. The particles corresponding to all solution fields are bosons. As expected from QED, if the coupling constant converges to zero, then so does the mass gap. The results are proved first for the model with the bare coupling constant, and then for a model with a running coupling constant by means of renormalization.Comment: With respect to the preceding version of this paper, the gauge invariance of the construction has been proved and the construction of the probability measure making the Hamiltonian QCD selfadjoint has been rewritten with more clarit

Managing the island territory : a historical perspective on sub-state nationalism in Corsica and Sardinia

Corsica (France) and Sardinia (Italy) are two islands of the western Mediterranean basin separated by a narrow strait. They share a problematic relationship with the mainland states to which they are associated, and from which they obtained their status of subnational island jurisdiction (SNIJ). The metropole/island relationship of these two islands is characterized by centrifugal tensions and the presence of sub-state nationalisms. These movements are different in terms of characteristics, strategies and electoral results, because of how France and Italy have managed the integration of the two islands, how the two island nationalisms have evolved, and how both metropolitan states have dealt with them. This article proposes a comparative history of Sardinian and Corsican nationalism and the relationship of Italy and France with these island territories. The intention is to analyse the two nationalisms, based almost exclusively on political science, with an historical perspective, highlighting the impact caused by the central states’ attitudes. In this way, the article points out how the differences between the political context of the two islands is defined by the different approach taken by France and Italy in managing their island territories.peer-reviewe

Numerical solution of the radiative transfer equation: X-ray spectral formation from cylindrical accretion onto a magnetized neutron star

Predicting the emerging X-ray spectra in several astrophysical objects is of great importance, in particular when the observational data are compared with theoretical models. To this aim, we have developed an algorithm solving the radiative transfer equation in the Fokker-Planck approximation when both thermal and bulk Comptonization take place. The algorithm is essentially a relaxation method, where stable solutions are obtained when the system has reached its steady-state equilibrium. We obtained the solution of the radiative transfer equation in the two-dimensional domain defined by the photon energy E and optical depth of the system tau using finite-differences for the partial derivatives, and imposing specific boundary conditions for the solutions. We treated the case of cylindrical accretion onto a magnetized neutron star. We considered a blackbody seed spectrum of photons with exponential distribution across the accretion column and for an accretion where the velocity reaches its maximum at the stellar surface and at the top of the accretion column, respectively. In both cases higher values of the electron temperature and of the optical depth tau produce flatter and harder spectra. Other parameters contributing to the spectral formation are the steepness of the vertical velocity profile, the albedo at the star surface, and the radius of the accretion column. The latter parameter modifies the emerging spectra in a specular way for the two assumed accretion profiles. The algorithm has been implemented in the XSPEC package for X-ray spectral fitting and is specifically dedicated to the physical framework of accretion at the polar cap of a neutron star with a high magnetic field (> 10^{12} G), which is expected to be typical of accreting systems such as X-ray pulsars and supergiant fast X-ray transients.Comment: 13 pages, 20 figures, accepted for publication in A&