90,487 research outputs found

    Wavelet Electrodynamics I

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    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

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    Using the two-loop approximation of chiral perturbation theory, we calculate the momentum and density dependent isovector nuclear spin-orbit strength Vls(p,kf)V_{ls}(p,k_f). This quantity is derived from the spin-dependent part of the interaction energy Σspin=i2σ(q×p)[Uls(p,kf)Vls(p,kf)τ3δ]\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 1π1\pi-exchange generates at saturation density, kf0=272.7k_{f0}=272.7 MeV, an isovector nuclear spin-orbit strength at p=0p=0 of Vls(0,kf0)50V_{ls}(0,k_{f0}) \simeq 50 MeVfm2^2. This value is about 1.4 times the analogous isoscalar nuclear spin-orbit strength Uls(0,kf0)35U_{ls}(0,k_{f0})\simeq 35 MeVfm2^2 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 Uls(p,kf)U_{ls}(p,k_f). The effects of the three-body diagrams constructed from the Weinberg-Tomozawa ππNN\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

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    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

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    Based on a recent chiral approach to nuclear matter we calculate the in-medium interaction of nucleons at the Fermi surface p1,2=kf|\vec p_{1,2}|=k_f. The isotropic part of this quasi-particle interaction is characterized by four density dependent (dimensionful) Fermi-liquid parameters: f0(kf),f0(kf),g0(kf)f_0(k_f), f_0'(k_f), g_0(k_f) and g0(kf)g_0'(k_f). In the approximation to 1π1\pi-exchange and iterated 1π1\pi-exchange (which as such leads already to a good nuclear matter equation of state) we find a spin-isospin interaction strength of g0(2mπ)=1.14g_0'(2m_\pi) = 1.14 fm2^2, compatible with existing empirical values. In the next step we include systematically the contributions from 2π2\pi-exchange with virtual Δ(1232)\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 g0(kf0)g_0(k_{f0}) and g0(kf0)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 g0(kf0)g_0(k_{f0}) and g0(kf0)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 1π1\pi-exchange tensor interaction we find from the 2π2\pi-exchange corrections almost a doubling of the isoscalar tensor strength h0(kf)h_0(k_f), whereas the isovector tensor strength h0(kf)h_0'(k_f) is much less affected. These features are not changed by the inclusion of the chiral πNΔ\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

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    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

    Ultrafast coherent spectroscopy

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    Making electromagnetic wavelets

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    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

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    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 62.362.3 MeV at r=1.0r=1.0 fm. There is a similarly strong isovector central attraction which however originates mainly from the third order low energy constants dˉj\bar d_j entering the chiral πN\pi N-scattering amplitude. We also evaluate the one-loop 2π2\pi-exchange diagram with two second order chiral ππNN\pi \pi NN-vertices proportional to the low energy constants c1,2,3,4c_{1,2,3,4} as well as the first relativistic 1/M-correction to the 2π2\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

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    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
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