Second order formalism for spin 1/2 fermions and Compton scattering

We develop a second order formalism for spin 1/2 fermions based on the projection over Poincar\'{e} invariant subspaces in the $(1/2,0)\oplus(0,1/2)$ representation of the homogeneous Lorentz group. Using $U(1)_{em}$ gauge principle we obtain second order description for the electromagnetic interactions of a spin 1/2 fermion with two free parameters, the gyromagnetic factor $g$ and a parameter $\xi$ related to odd-parity Lorentz structures. We calculate Compton scattering in this formalism. In the particular case $g=2, \xi=0$ and for states with well defined parity we recover Dirac results. In general, we find the correct classical limit and a finite value $r_{c}^{2}$ for the forward differential cross section, independent of the photon energy and of the value of the parameters $g$ and $\xi$. The differential cross section vanishes at high energies for all $g, \xi$ except in the forward direction. The total cross section at high energies vanishes only for $g=2, \xi=0$. We argue that this formalism is more convenient than Dirac theory in the description of low energy electromagnetic properties of baryons and illustrate the point with the proton case.Comment: 11 pages 4 figure

The Correlated Block Renormalization Group

We formulate the standard real-space renormalization group method in a way which takes into account the correlation between blocks. This is achieved in a dynamical way by means of operators which reflect the influence on a given block of its neighbours. We illustrate our method in the example of the tight-binding model in 1D and 2D for various types of boundary conditions.Comment: LATEX file, 18 pages, 7 figures available upon reques

Integration brings convergence? The role of public and human capital

This work decompose labor-productivity grotwh and convergence in EU into components attributable to technological change (shifts in the European production frontier), technological catch-up (movements toward or away from the frontier) and factor accumulation (movement toward or away from the frontier). This work extends previous researchs considering public capital and human capitas as additional productive inputs and analysing its separate constribution to convergence as components of factor accumulation. In the case of human capital, we also test its rate effect as determinant factor of technical change. With this purpose we applied the Malmquist index of total factor productivity to an European data base to provide evidence for the 15 EU State Members. The results show that growth is primarily driven by factor accumulation which contribution is fundamental for lagging countries. We do not find evidence of any significant convergence over the whole period studied related to integration with factor accumulation and efficiency change as important factors of convergence while technical change (encouraged by greater human capital) has worked against it. Key words: Human Capital, Malmquist Index, Source of Convergence. JEL Classification: O47 H54 D24

Tribological behaviour of the low and high viscosity peek against steel using different contact pressures

In the market of polymers for tribological applications polyetheretherketone (PEEK) are often used for satisfying requests coming from industry regarding enhanced properties such as, thermal stability, friction and wear resistance. These properties promote the material to be used in so called high performance tribological applications. However, fundamental mechanisms governing friction and wear are not yet fully understood and neither is the influence of composition parameters. An important parameter is PEEK’s viscosity during manufacturing process which is heated up to semi-solid state, between its glass transition and melting temperature. This paper studies the friction and wear performance of low and high viscosity PEEK and pure PEEK under dry reciprocating sliding contact. The tests were performed in large scale specimens under flat-on-flat configuration to determine the transitions in tribological behaviour at different contact pressures. Tests were carried out at controlled atmosphere with 25 °C and a relative humidity of 50%. Contact pressures parameters were 4, 8 and 10 MPa used at a sliding speed of 20 mm/s. Post mortem analyses were carried out by means of 2-D surface topography and optical microscopy. The results show that the pure PEEK exhibits low coefficient of friction and wear rate when the contact pressure increase and similar behave for high and low viscosity PEEK