Landau Migdal Theory of Interacting Fermi Systems: A Framework for Effective Theories in Nuclear Structure Physics

We review Migdal's Theory of Finite Fermi Systems and its application to the structure of nuclei. The theory is an extension of Landau's Theory of Interacting Fermi Systems. In the first part the basic formulas are derived within the many body Green functions approach. The theory is applied to isovector electric giant resonances in medium and heavy mass nuclei. The parameterizations of the enormalized effective ph-interaction and the effective operators are discussed. It is shown that the number of free parameters are restricted due to conservation laws. We also present an extension of Migdal's theory, where the low-lying phonons are considered in a consistent manner. The extended theory is again applied to the same isovector electric giant resonances and to the analysis of $(\alpha,\alpha^\prime)$ reaction data. We point out that the extended theory is the appropriate frame for self consistent nuclear structure calculations starting from effective Lagrangians and Hamiltonians.Comment: 6 figure

From soft to hard regime in elastic pion-pion scattering above resonances

We discuss the onset of the dominance of the Glauber-Gribov-Landshoff (GGL) component of pQCD hard two-gluon (2G) exchange contribution to hard elastic $\pi\pi$ scattering at moderate energies . Such a hard $\pi\pi$ scattering could via final state interaction on the $\gamma \gamma \to \pi^+ \pi^-$ reaction in which pQCD quark-exchange contribution is known to be short of strength. While in the nonrelativistic approximation the GGL amplitude is known to be free of suppression by the pion form factor, we show that in the relativistic light-cone approach it acquires a residual, albeit a weak, suppression. Furthermore,z the same mechanism it is free of the end-point contributions. We evaluation the GGL amplitude with a model light-cone wave function consistent with the pion charge form factor data. The soft contribution to elastic $\pi\pi$ scattering is estimated based on the $NN$ and $\pi N$ total cross section data and Regge factorization, which gives the $\pi\pi$ total cross sections consistent with the ones deduced earlier from the absorption model analysis of the $\pi N \to X N, X \Delta$ data. We evaluate the large-$|t|$ tail of the soft amplitude within the Regge absorption models. We find that while in the same sign $\pi^\pm\pi^\pm$ scattering the hard GGL mechanism takes over at |t|\gsim 3 GeV$^{-2}$, in the opposite-sign $\pi^\pm\pi^\mp$ scattering the hard GGL mechanism |t|\lsim 4 GeV$^{-2}$.Comment: 16 pages, 11 figure

Current log-periodic view on future world market development

Applicability of the concept of financial log-periodicity is discussed and encouragingly verified for various phases of the world stock markets development in the period 2000-2010. In particular, a speculative forecasting scenario designed in the end of 2004, that properly predicted the world stock market increases in 2007, is updated by setting some more precise constraints on the time of duration of the present long-term equity market bullish phase. A termination of this phase is evaluated to occur in around November 2009. In particular, on the way towards this dead-line, a Spring-Summer 2008 increase is expected. On the precious metals market a forthcoming critical time signal is detected at the turn of March/April 2008 which marks a tendency for at least a serious correction to begin. In the present extended version some predictions for the future oil price are incorporated. In particular a serious correction on this market is expected to start in the coming days.Comment: presented by S. Drozdz at FENS2007 conference, 10 pages, 6 Figs, an extended version with the oil market included (Fig.7

Towards identifying the world stock market cross-correlations: DAX versus Dow Jones

Effects connected with the world globalization affect also the financial markets. On a way towards quantifying the related characteristics we study the financial empirical correlation matrix of the 60 companies which both the Deutsche Aktienindex (DAX) and the Dow Jones (DJ) industrial average comprised during the years 1990-1999. The time-dependence of the underlying cross-correlations is monitored using a time window of 60 trading days. Our study shows that if the time-zone delays are properly accounted for the two distant markets largely merge into one. This effect is particularly visible during the last few years. It is however the Dow Jones which dictates the trend.Comment: LaTeX, 6 pages, 8 figure