We discuss the limits of applying spectroscopic methods for the determination of magnetic fields that are based on the Zeeman effect and allow for extending the field diagnostics to conditions inwhich the Zeemansplit pattern is not resolvable. We analyze the diagnostic limits in terms of the minimummagnetic field that canbedetermined for a givenLorentzian line-width. This formof analysis isusef...

A general class of Lorentzian metrics, M0 × R 2 , ·, ·z = ·, ·x + 2 du dv + H(x, u) du 2 , with (M0, ·, ·x) any Riemannian mani-fold, is introduced in order to generalize classical exact plane fronted waves. Here, we start a systematic study of their main geodesic properties: geodesic completeness, geodesic connectedness and multiplicity or causal character of connecting geodesics. These result...

The point-spread function (PSF) of a fiber-optic taper-coupled CCD area detector was measured over five decades of intensity using a 20 µm X-ray beam and ~2000-fold averaging. The `tails' of the PSF clearly revealed that it is neither Gaussian nor Lorentzian, but instead resembles the solid angle subtended by a pixel at a point source of light held a small distance (~27 µm) above the pixel plan...

We argue that the Lorentzian path integral is a better starting point for quantum cosmology than its Euclidean counterpart. In particular, we revisit the minisuperspace calculation of the Feynman path integral for quantum gravity with a positive cosmological constant. Instead of rotating to Euclidean time, we deform the contour of integration over metrics into the complex plane, exploiting Pica...

Dirac fermions on a two-dimensional lattice with disorder are considered. The Dirac mass, which controls the gap between the two bands of the fermions, is subject to random fluctuations. Another type of disorder is discussed presented by a random vector potential. It is shown that the imaginary part of the one-particle Green’s function can be written as the imaginary part of another Green’s fun...

We study the large λ limit of the loop-dependent characteristic functional Z(λ) =< exp(iλ ∮ c ~v ·d~x) >, related to the probability density function (PDF) of the circulation around a closed contour c. The analysis is carried out in the framework of the Martin-Siggia-Rose field theory formulation of the turbulence problem, by means of the saddle-point technique. Axisymmetric instantons, labelle...

A general class of Lorentzian metrics, M0 ×R, 〈·, ·〉z = 〈·, ·〉x + 2 du dv + H (x, u) du2, with (M0, 〈·, ·〉x ) any Riemannian manifold, is introduced in order to generalize classical exact plane fronted waves. Here, we start a systematic study of their main geodesic properties: geodesic completeness, geodesic connectedness and multiplicity causal character of connecting geodesics. These results ...

The theory of gravitational lensing is reviewed from a spacetime perspective, without quasi-Newtonian approximations. More precisely, the review covers all aspects of gravitational lensing where light propagation is described in terms of lightlike geodesics of a metric of Lorentzian signature. It includes the basic equations and the relevant techniques for calculating the position, the shape, a...