Wavelet Electrodynamics I

A new representation for solutions of Maxwell's equations is derived. Instead of being expanded in plane waves, the solutions are given as linear superpositions of spherical wavelets dynamically adapted to the Maxwell field and well-localized in space at the initial time. The wavelet representation of a solution is analogous to its Fourier representation, but has the advantage of being local. It is closely related to the relativistic coherent-state representations for the Klein-Gordon and Dirac fields developed in earlier work.Comment: 8 Pages in Plain Te

Isovector nuclear spin-orbit interaction from chiral pion-nucleon dynamics

Using the two-loop approximation of chiral perturbation theory, we calculate the momentum and density dependent isovector nuclear spin-orbit strength $V_{ls}(p,k_f)$. This quantity is derived from the spin-dependent part of the interaction energy $\Sigma_{spin} = {i\over 2} \vec \sigma \cdot (\vec q \times\vec p)[U_{ls}(p,k_f)- V_{ls}(p,k_f)\tau_3 \delta]$ of a nucleon scattering off weakly inhomogeneous isospin-asymmetric nuclear matter. We find that iterated $1\pi$-exchange generates at saturation density, $k_{f0}=272.7$MeV, an isovector nuclear spin-orbit strength at $p=0$ of $V_{ls}(0,k_{f0}) \simeq 50$ MeVfm$^2$. This value is about 1.4 times the analogous isoscalar nuclear spin-orbit strength $U_{ls}(0,k_{f0})\simeq 35$ MeVfm$^2$ generated by the same two-pion exchange diagrams. We also calculate several relativistic 1/M-corrections to the isoscalar nuclear spin-orbit strength. In particular, we evaluate the contributions from irreducible two-pion exchange to $U_{ls}(p,k_f)$. The effects of the three-body diagrams constructed from the Weinberg-Tomozawa $\pi\pi NN$-contact vertex on the isoscalar nuclear spin-orbit strength are computed. We find that such relativistic 1/M-corrections are less than 20% of the isoscalar nuclear spin-orbit strength generated by iterated one-pion-exchange, in accordance with the expectation from chiral power counting.Comment: 15 pages, 8 figure

Multi-frequency observations as a key to source and environment parameters of FRII objects

Our knowledge of the environments of radio-loud AGN is still sketchy. However, to understand the jet phenomenon it is important to know about the properties of the surroundings in which jets are formed and evolve. Here I present an analytical model of the radio surface brightness distribution of the large scale structure of FRII-type radio sources. The `virtual maps' resulting from this model can be compared with observed maps to obtain estimates for a range of source properties from the model. These properties include parameters describing the gas density distribution of the source environment, the energy transport rate of the jets and the orientation angle of the source jet axis with respect to the line of sight. The model is tested using radio maps of Cygnus A for which there are independent measurements of some of these parameters available in the literature. The model estimates agree well with these observations. Varying the resolution of the radio maps used in thecomparison does not change the results significantly.Comment: 10 pages, 2 figures, to appear in `Life Cycles of Radio Galaxies', ed. J. Biretta et al., New Astronomy Review

Quasi-particle interaction in nuclear matter from chiral pion-nucleon dynamics

Based on a recent chiral approach to nuclear matter we calculate the in-medium interaction of nucleons at the Fermi surface $|\vec p_{1,2}|=k_f$. The isotropic part of this quasi-particle interaction is characterized by four density dependent (dimensionful) Fermi-liquid parameters: $f_0(k_f), f_0'(k_f), g_0(k_f)$ and $g_0'(k_f)$. In the approximation to $1\pi$-exchange and iterated $1\pi$-exchange (which as such leads already to a good nuclear matter equation of state) we find a spin-isospin interaction strength of $g_0'(2m_\pi) = 1.14$fm$^2$, compatible with existing empirical values. In the next step we include systematically the contributions from $2\pi$-exchange with virtual $\Delta(1232)$-isobar excitation which have been found important for good single-particle properties and spin-stability of nuclear matter. Without any additional short distance terms the spin-dependent Fermi-liquid parameters $g_0(k_{f0})$ and $g'_0(k_{f0})$ come out far too large. Estimates of these short-distance parameters from realistic NN-potentials go in the right direction, but sizeable enhancement factors are still needed to reproduce the empirical values of $g_0(k_{f0})$ and $g_0'(k_{f0})$. This points towards the importance of higher order iterations subsumed in the induced interaction. We consider also the tensor part of the quasi-nucleon interaction at the Fermi surface. In comparison to the leading $1\pi$-exchange tensor interaction we find from the $2\pi$-exchange corrections almost a doubling of the isoscalar tensor strength $h_0(k_f)$, whereas the isovector tensor strength $h_0'(k_f)$ is much less affected. These features are not changed by the inclusion of the chiral $\pi N\Delta$-dynamics.Comment: 19 pages, 9 figures, to be published in Nuclear Physics A (2006

Erratum: Luminosity function, sizes and FR dichotomy of radio-loud AGN

This erratum corrects a number of formulae containing mistakes in the paper 'Luminosity function, sizes and FR dichotomy of radio-loud AGN', 2007, MNRAS, v. 381, p.1548. The corrections do not alter any of the conclusions in the original paper.Comment: single page, no figures, erratum to MNRAS, 2007, v. 381, p. 154

Making electromagnetic wavelets

Electromagnetic wavelets are constructed using scalar wavelets as superpotentials, together with an appropriate polarization. It is shown that oblate spheroidal antennas, which are ideal for their production and reception, can be made by deforming and merging two branch cuts. This determines a unique field on the interior of the spheroid which gives the boundary conditions for the surface charge-current density necessary to radiate the wavelets. These sources are computed, including the impulse response of the antenna.Comment: 29 pages, 4 figures; minor corrections and addition

Chiral 2π2\pi-exchange NN-potentials: Two-loop contributions

We calculate in heavy baryon chiral perturbation theory the local NN-potentials generated by the two-pion exchange diagrams at two-loop order. We give explicit expressions for the mass-spectra (or imaginary parts) of the corresponding isoscalar and isovector central, spin-spin and tensor NN-amplitudes. We find from two-loop two-pion exchange a sizeable isoscalar central repulsion which amounts to $62.3$MeV at $r=1.0$fm. There is a similarly strong isovector central attraction which however originates mainly from the third order low energy constants $\bar d_j$ entering the chiral $\pi N$-scattering amplitude. We also evaluate the one-loop $2\pi$-exchange diagram with two second order chiral $\pi \pi NN$-vertices proportional to the low energy constants $c_{1,2,3,4}$ as well as the first relativistic 1/M-correction to the $2\pi$-exchange diagrams with one such vertex. The diagrammatic results presented here are relevant components of the chiral NN-potential at next-to-next-to-next-to-leading order.Comment: 6 pages, 2 figure

Deformation of string topology into homotopy skein modules

Relations between the string topology of Chas and Sullivan and the homotopy skein modules of Hoste and Przytycki are studied. This provides new insight into the structure of homotopy skein modules and their meaning in the framework of quantum topology. Our results can be considered as weak extensions to all orientable 3-manifolds of classical results by Turaev and Goldman concerning intersection and skein theory on oriented surfaces.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-34.abs.htm