Parity realization in Vector-like theories from Fermion Bilinears

We reconsider in this paper the old aim of trying to understand if the observed realization of discrete symmetries as Parity or CP in the QCD vacuum can be satisfied from first principles. We show how under the appropriate assumptions implicitely done by Vafa and Witten in their old paper on parity realization in vector-like theories, all parity and CP odd operators constructed from fermion bilinears of the form $\bar\psi\tilde O\psi$ should take a vanishing vacuum expectation value in a vector-like theory with N degenerate flavours (N>1). In our analysis the Vafa-Witten theorem on the impossibility to break spontaneously the flavour symmetry in a vector-like theory plays a fundamental role.Comment: 12 pages, no figures To be published in JHE

Dynamical Symmetry Breaking in Planar QED

We investigate (2+1)-dimensional QED coupled with Dirac fermions both at zero and finite temperature. We discuss in details two-components (P-odd) and four-components (P-even) fermion fields. We focus on P-odd and P-even Dirac fermions in presence of an external constant magnetic field. In the spontaneous generation of the magnetic condensate survives even at infinite temperature. We also discuss the spontaneous generation of fermion mass in presence of an external magnetic field.Comment: 34 pages, 8 postscript figures, final version to appear on J. Phys.

A new orthogonalization procedure with an extremal property

Various methods of constructing an orthonomal set out of a given set of linearly independent vectors are discussed. Particular attention is paid to the Gram-Schmidt and the Schweinler-Wigner orthogonalization procedures. A new orthogonalization procedure which, like the Schweinler- Wigner procedure, is democratic and is endowed with an extremal property is suggested.Comment: 7 pages, latex, no figures, To appear in J. Phys

Highlighting Current Trends in Volunteered Geographic Information

Volunteered Geographic Information (VGI) is a growing area of research. This Special Issue aims to capture the main trends in VGI research based on 16 original papers, and distinguishes between two main areas, i.e., those that deal with the characteristics of VGI and those focused on applications of VGI. The topic of quality assessment and assurance dominates the papers on VGI characteristics, whereas application-oriented work covers three main domains: human behavioral analysis, natural disasters, and land cover/land use mapping. In this Special Issue, therefore, both the challenges and the potentials of VGI are addressed

One-loop Beta Functions for the Orientable Non-commutative Gross-Neveu Model

We compute at the one-loop order the beta-functions for a renormalisable non-commutative analog of the Gross Neveu model defined on the Moyal plane. The calculation is performed within the so called x-space formalism. We find that this non-commutative field theory exhibits asymptotic freedom for any number of colors. The beta-function for the non-commutative counterpart of the Thirring model is found to be non vanishing.Comment: 16 pages, 9 figure

Thiemann transform for gravity with matter fields

The generalised Wick transform discovered by Thiemann provides a well-established relation between the Euclidean and Lorentzian theories of general relativity. We extend this Thiemann transform to the Ashtekar formulation for gravity coupled with spin-1/2 fermions, a non-Abelian Yang-Mills field, and a scalar field. It is proved that, on functions of the gravitational and matter phase space variables, the Thiemann transform is equivalent to the composition of an inverse Wick rotation and a constant complex scale transformation of all fields. This result holds as well for functions that depend on the shift vector, the lapse function, and the Lagrange multipliers of the Yang-Mills and gravitational Gauss constraints, provided that the Wick rotation is implemented by means of an analytic continuation of the lapse. In this way, the Thiemann transform is furnished with a geometric interpretation. Finally, we confirm the expectation that the generator of the Thiemann transform can be determined just from the spin of the fields and give a simple explanation for this fact.Comment: LaTeX 2.09, 14 pages, no figure

On the gravitational field of static and stationary axial symmetric bodies with multi-polar structure

We give a physical interpretation to the multi-polar Erez-Rozen-Quevedo solution of the Einstein Equations in terms of bars. We find that each multi-pole correspond to the Newtonian potential of a bar with linear density proportional to a Legendre Polynomial. We use this fact to find an integral representation of the $\gamma$ function. These integral representations are used in the context of the inverse scattering method to find solutions associated to one or more rotating bodies each one with their own multi-polar structure.Comment: To be published in Classical and Quantum Gravit